A291351 Numbers k such that k!4 + 2^10 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

9, 13, 23, 27, 33, 47, 61, 113, 145, 161, 191, 281, 291, 417, 869, 919, 1213, 1297, 1663, 2103, 2297, 2325, 3241, 3895, 4337, 6645, 7911, 8737, 13369, 13555, 19245, 34025, 47779, 48589, 54521, 91355

Offset: 1

Author

Robert Price, Aug 22 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 1069, 1609, 1515229, 40884559, 4996617649, ...

a(37) > 10^5.

Terms > 33 correspond to probable primes.

Examples

			13!4 + 2^10 = 13*9*5*1 + 1024 = 1609 is prime, so 13 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!4+1024.
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^10] &]
Select[Range[10^3],PrimeQ[Times@@Range[#,1,-4]+2^10]&] (* The program generates the first 16 terms of the sequence. *) (* Harvey P. Dale, Feb 08 2025 *)

Extensions

a(36)-a(37) from Robert Price, Sep 25 2019