A252788 Numbers m such that 3^m + m is a semiprime.

1, 4, 7, 14, 16, 20, 22, 32, 38, 55, 80, 92, 188, 220, 296, 328, 370, 422, 452, 454, 500, 650, 934, 962

Offset: 1

Author

Vincenzo Librandi, Dec 22 2014

Keywords

• nonn
• more

Comments

a(21) >= 500. - Hugo Pfoertner, Aug 03 2019

From Kevin P. Thompson, Apr 24 2022: (Start)

a(25) >= 1402.

m=1448 is also a term of this sequence. (End)

Examples

			1 is in this sequence because 3^1+1 = 2*2 is semiprime.
14 is in this sequence because 3^14+14 = 283*16901 and these two factors are prime.
		

Links

• factordb.com, Status of 3^500+500.
• factordb.com, Status of 3^1402+1402.

Crossrefs

Cf. numbers m such that k^m+m is a semiprime: A085745 (k=2), this sequence (k=3), A252789 (k=4), A252790 (k=5), A252791 (k=6), A252792 (k=7), A252793 (k=8), A252794 (k=9), A252795 (k=10).

Cf. A252656.

Programs

Magma

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

Mathematica

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

PARI

first(m)=my(v=vector(m),r=1);for(i=1,m,while(bigomega(3^r + r)!=2,r++);v[i]=r;r++);v; \\ Anders Hellström, Aug 14 2015

Extensions

a(13)-a(16) from Luke March, Jul 18 2015

a(17)-a(20) from Carl Schildkraut, Aug 19 2015

a(21)-a(24) from Kevin P. Thompson, Apr 24 2022