A291345 Numbers k such that k!4 + 2^5 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

5, 7, 11, 13, 19, 21, 25, 27, 35, 37, 51, 55, 65, 71, 105, 107, 129, 223, 229, 273, 307, 337, 345, 479, 509, 517, 519, 921, 963, 993, 1309, 1697, 1855, 1871, 2451, 2573, 2755, 3059, 3271, 4005, 4823, 17079, 20209, 20559, 37845, 38343, 68383, 79617, 81539

Offset

1,1

Comments

Corresponding primes are: 37, 53, 263, 617, 65867, 208877, 5221157, 40883567, ...

a(50) > 10^5.

Terms > 37 correspond to probable primes.

Links

Table of n, a(n) for n=1..49.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+32.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

13!4 + 2^5 = 13*9*5*1 + 32 = 617 is prime, so 13 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^5] &]
Select[Range[82000], PrimeQ[Times@@Range[#, 1, -4]+32]&] (* Harvey P. Dale, Apr 11 2022 *)

Crossrefs

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

Sequence in context: A246463 A314297 A108409 * A298867 A039681 A375170

Adjacent sequences: A291342 A291343 A291344 * A291346 A291347 A291348

Keyword

nonn,more

Author

Robert Price, Aug 22 2017

Extensions

a(47)-a(49) from Robert Price, Sep 25 2019

Status

approved