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A291348

Numbers k such that k!4 + 2^7 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

3, 7, 9, 11, 15, 19, 29, 37, 91, 123, 151, 197, 415, 763, 1817, 2981, 3977, 4199, 11667, 12865, 16873, 19449, 27213, 31581, 64877, 65401

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OFFSET

1,1

COMMENTS

Corresponding primes are: 131, 149, 173, 359, 3593, 65963, 151412753, ...

a(27) > 10^5.

Terms > 37 correspond to probable primes.

LINKS

OpenPFGW Project, Primality Tester

EXAMPLE

15!4 + 2^7 = 15*11*7*3*1 + 128 = 3593 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] + 2^7] &]

Select[Range[3000], PrimeQ[Times@@Range[#, 1, -4]+128]&] (* Harvey P. Dale, Feb 26 2023 *)

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Robert Price, Aug 22 2017

EXTENSIONS

a(25)-a(26) from Robert Price, Sep 25 2019

STATUS

approved