A291347 Numbers k such that k!4 + 2^6 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

3, 9, 15, 17, 19, 29, 31, 45, 55, 63, 73, 101, 135, 173, 217, 271, 439, 535, 729, 787, 933, 1473, 1651, 6617, 7805, 12461, 13253, 18627, 20243, 55271

Offset

1,1

Comments

Corresponding primes are: 67, 109, 3529, 10009, 65899, 151412689, 1267389649, ...

a(31) > 10^5.

Terms > 31 correspond to probable primes.

Links

Table of n, a(n) for n=1..30.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+64.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

15!4 + 2^6 = 15*11*7*3*1 + 64 = 3529 is prime, so 15 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^6] &]

Crossrefs

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

Sequence in context: A273323 A061966 A085328 * A062220 A310328 A043381

Adjacent sequences: A291344 A291345 A291346 * A291348 A291349 A291350

Keyword

nonn,more

Author

Robert Price, Aug 22 2017

Extensions

a(30) from Robert Price, Sep 25 2019

Status

approved