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A242269
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Numbers n such that n*6^n+1 is semiprime.
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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
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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];
(PARI) is(n)=bigomega(n*6^n+1)==2 \\ _Anders Hellström_, Aug 28 2015
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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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_Vincenzo Librandi_, May 10 2014
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EXTENSIONS
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a(19)-a(30) from _Carl Schildkraut_, Aug 28 2015
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STATUS
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approved
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