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Numbers n such that n*3^n + 1 is semiprime.
7

%I #31 Sep 08 2022 08:46:08

%S 1,3,10,16,20,22,24,34,39,56,63,108,128,194,202,212,214,218,314,364,

%T 662,722

%N Numbers n such that n*3^n + 1 is semiprime.

%C The semiprimes of this form are 4, 82, 590491, 688747537, 69735688021, 690383311399, 6778308875545, 567024177788663347, 158049650967740074414, 29307467449532190083956645177, ...

%C a(23) >= 894. - _Hugo Pfoertner_, Aug 03 2019

%H <a href="http://factordb.com/index.php?query=894*3%5E894%2B1">Status of 894*3^894+1 in factordb.com</a>.

%t Select[Range[130], PrimeOmega[# 3^# + 1] == 2 &]

%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..130] | IsSemiprime(s) where s is n*3^n+1];

%o (PARI) isok(n) = bigomega(n*3^n + 1)==2; \\ _Michel Marcus_, Mar 30 2019

%Y Cf. numbers n such that n*k^n + 1 is semiprime: A242175 (k=2), this sequence (k=3), A242204 (k=4), A242205 (k=5), A242269 (k=6), A242270 (k=7), A242271 (k=8), A242272 (k=9), A216378 (k=10).

%Y Cf. A006552, A050914.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, May 10 2014

%E a(14)-a(20) from _Luke March_, Jul 30 2015

%E a(21)-a(22) from _Daniel Suteu_, Mar 30 2019