Search: a242176 -id:a242176
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A242177
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Numbers k such that k*7^k + 1 is prime.
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+10
4
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Select[Range[3500], PrimeQ[# 7^# + 1] &]
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PROG
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(Magma) [n: n in [0..3500] | IsPrime(n*7^n+1)];
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CROSSREFS
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Cf. similar sequences listed in A242176.
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KEYWORD
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nonn,more,bref
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A242178
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Numbers k such that k*8^k + 1 is prime.
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+10
4
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Select[Range[2000], PrimeQ[# 8^# + 1] &]
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PROG
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(Magma) [n: n in [0..2000] | IsPrime(n*8^n+1)];
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CROSSREFS
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Cf. similar sequences listed in A242176.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A242196
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Numbers k such that k*12^k + 1 is prime.
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+10
3
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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Select[Range[2300], PrimeQ[# 12^# + 1] &]
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PROG
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(Magma) [n: n in [0..2300] | IsPrime(n*12^n+1)]
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CROSSREFS
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Cf. similar sequences listed in A242176.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A242197
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Numbers k such that k*14^k + 1 is prime.
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+10
3
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3, 5, 6, 9, 33, 45, 243, 252, 1798, 2429, 5686, 12509, 42545
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Select[Range[2000], PrimeQ[# 14^# + 1] &]
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PROG
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(Magma) [n: n in [0..2000] | IsPrime(n*14^n+1)];
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CROSSREFS
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Cf. similar sequences listed in A242176.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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a(10)-a(13) from Loeh's list (see Links) - Bruno Berselli, May 08 2014
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STATUS
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approved
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A242198
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Numbers k such that k*15^k + 1 is prime.
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+10
3
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Select[Range[2000], PrimeQ[# 15^# + 1] &]
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PROG
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(Magma) [n: n in [0..2500] | IsPrime(n*15^n+1)];
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CROSSREFS
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Cf. similar sequences listed in A242176.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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a(7)-a(8) from Loeh's list (see Links)
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STATUS
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approved
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A242199
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Numbers k such that k*16^k + 1 is prime.
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+10
3
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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Select[Range[2000], PrimeQ[# 16^# + 1] &]
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PROG
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(Magma) [n: n in [0..2000] | IsPrime(n*16^n+1)];
(Sage) [n for n in (1..2000) if is_prime(n*16^n + 1)] # Bruno Berselli, May 09 2014
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CROSSREFS
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Cf. similar sequences listed in A242176.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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a(7)-a(8) from Loeh's list (see Links)
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STATUS
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approved
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A242269
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Numbers n such that n*6^n+1 is semiprime.
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+10
1
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3, 5, 11, 12, 18, 20, 21, 24, 25, 35, 43, 45, 53, 58, 61, 71, 73, 75, 123, 124, 140, 147, 157, 205, 208, 233, 243, 245, 293, 301
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The semiprimes of this form are: 649, 38881, 3990767617, 26121388033, 1828079220031489, 73123168801259521, 460675963447934977,...
464 is definitely in this sequence, however 436 may or may not be. - Carl Schildkraut, Aug 28 2015
A continuation in the range 302 ... 1000 would use all terms without "?" and potentially ?-marked terms corresponding to composites with unknown factorization: 436?, 464, 511?, 512, 613, 662?, 720, 730, 802?, 865?, 943. - Hugo Pfoertner, Aug 05 2019
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LINKS
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MATHEMATICA
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Select[Range[435], PrimeOmega[# 6^# + 1] == 2 &]
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PROG
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(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..435] | IsSemiprime(s) where s is n*6^n+1];
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CROSSREFS
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Cf. similar sequences listed in A242203.
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A265013
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Numbers n such that n*9^n + 1 is prime.
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+10
1
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OFFSET
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1,1
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COMMENTS
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LINKS
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MATHEMATICA
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Select[Range[100000], PrimeQ[# 9^# + 1] &]
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PROG
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(PARI) for(n=1, 100000, if(isprime(n*9^n+1), print1(n, ", ")))
(Magma) [n: n in [0..100000] | IsPrime(n*9^n+1)];
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CROSSREFS
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Cf. A005849, A006552, A007646, A242176, A242177, A242178, A007647, A242196, A242197, A242198, A242199, A007648.
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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A338412
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Numbers k such that k * 20^k + 1 is prime.
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+10
0
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OFFSET
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1,1
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COMMENTS
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a(6) > 219976.
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LINKS
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MATHEMATICA
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Select[Range[1, 10000], PrimeQ[n*20^n+1] &]
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PROG
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(PARI) for(n=1, 10000, if(isprime(n*20^n+1), print1(n, ", ")))
(Magma) [n: n in [1..10000] |IsPrime(n*20^n+1)]
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CROSSREFS
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Numbers k such that k * b^k + 1 is prime: A006093 (b=1), A005849 (b=2), A006552 (b=3), A007646 (b=4), A242176 (b=6), A242177 (b=7), A242178 (b=8), A265013 (b=9), A007647(b=10), A242196(b=12), A242197 (b=14), A242198 (b=15), A242199 (b=16), A007648 (b=18), this sequence (b=20).
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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