A114970 Numbers m such that 2^m + m^2 is a semiprime.

5, 7, 17, 25, 43, 61, 69, 73, 105, 111, 117, 123, 135, 141, 171, 219, 231, 241, 309, 321, 543, 739, 795, 833, 975

Offset: 1

Author

Zak Seidov, Feb 22 2006

Keywords

• nonn
• more
• hard

Comments

a(26) >= 1125. - Tyler Busby, Dec 27 2024

Examples

			2^5 + 5^2 = 32 + 25 = 57 = 3*19 (semiprime).
		

Links

• factordb.com, Status of 2^1125+1125^2.

Crossrefs

Cf. A114971, A114973, A114974.

Programs

Magma

IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [1..175]|IsSemiprime(2^n+n^2)]; // Vincenzo Librandi, Dec 16 2010

Mathematica

Select[Range[200], PrimeOmega[2^# + #^2]==2&] (* Vincenzo Librandi, May 21 2014 *)

Extensions

a(16)-a(21) from Luke March, Jul 27 2015

a(22) from Hugo Pfoertner, Jul 28 2019

a(23)-a(25) from Tyler Busby, Dec 27 2024