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

1,2

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)

Links

Table of n, a(n) for n=1..24.

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

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

Example

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.

Mathematica

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

Prog

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

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.

Sequence in context: A310851 A310852 A072031 * A310853 A310854 A310855

Adjacent sequences: A252785 A252786 A252787 * A252789 A252790 A252791

Keyword

nonn,more

Author

Vincenzo Librandi, Dec 22 2014

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

Status

approved