A115398 Numbers k such that both k^2+1 and 2^k + 1 are semiprimes.

3, 5, 11, 12, 19, 28, 61, 64, 79, 92, 101, 104, 199, 356, 596, 692, 1709, 3539, 3824

Offset

1,1

Comments

Intersection of A085722 and A092559.

Links

Table of n, a(n) for n=1..19.

Example

11 is a term because 11^2 + 1 = 122 = 2*61 (semiprime) and 2^11 + 1 = 2049 = 3*683 (semiprime).

Mathematica

Select[Range[700], PrimeOmega[#^2+1]==PrimeOmega[2^#+1]==2&] (* Harvey P. Dale, Apr 14 2019 *)

Prog

(PARI) isok(n) = (bigomega(n^2+1) == 2) && (bigomega(2^n+1) == 2); \\ Michel Marcus, Oct 10 2013
(Magma) IsSemiprime:=func<n | &+[k[2]: k in Factorization(n)] eq 2>; [n: n in [2..700] | IsSemiprime(n^2+1) and IsSemiprime(2^n+1)]; // Vincenzo Librandi, Oct 10 2013

Crossrefs

Cf. A085722, A092559.

Sequence in context: A072063 A242269 A309426 * A014597 A357369 A130603

Adjacent sequences: A115395 A115396 A115397 * A115399 A115400 A115401

Keyword

nonn,more

Author

Zak Seidov, Mar 08 2006

Extensions

a(17)-a(19) from Robert Israel, Nov 27 2023

Status

approved