A115398 - OEIS

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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

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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