A242269 Numbers n such that n*6^n+1 is semiprime.

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

Offset: 1

Author

Vincenzo Librandi, May 10 2014

Keywords

• nonn
• more
• hard

Comments

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

Links

• factordb.com, Status of 436*6^436+1.

Crossrefs

Cf. similar sequences listed in A242203.

Cf. A050917, A242176.

Programs

Magma

IsSemiprime:=func; [n: n in [1..435] | IsSemiprime(s) where s is n*6^n+1];

Mathematica

Select[Range[435], PrimeOmega[# 6^# + 1] == 2 &]

PARI

is(n)=bigomega(n*6^n+1)==2 \\ Anders Hellström, Aug 28 2015

Extensions

a(19)-a(30) from Carl Schildkraut, Aug 28 2015