A242203 Numbers n such that n*3^n + 1 is semiprime.

1, 3, 10, 16, 20, 22, 24, 34, 39, 56, 63, 108, 128, 194, 202, 212, 214, 218, 314, 364, 662, 722

Offset: 1

Author

Vincenzo Librandi, May 10 2014

Keywords

• nonn
• more

Comments

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

a(23) >= 894. - Hugo Pfoertner, Aug 03 2019

Links

• Status of 894*3^894+1 in factordb.com.

Crossrefs

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).

Cf. A006552, A050914.

Programs

Magma

IsSemiprime:=func; [n: n in [1..130] | IsSemiprime(s) where s is n*3^n+1];

Mathematica

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

PARI

isok(n) = bigomega(n*3^n + 1)==2; \\ Michel Marcus, Mar 30 2019

Extensions

a(14)-a(20) from Luke March, Jul 30 2015

a(21)-a(22) from Daniel Suteu, Mar 30 2019