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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

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OFFSET

1,1

COMMENTS

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

a(37) > 10^5.

Terms > 33 correspond to probable primes.

LINKS

Table of n, a(n) for n=1..36.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+1024.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

EXAMPLE

13!4 + 2^10 = 13*9*5*1 + 1024 = 1609 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] + 2^10] &]

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 *)

CROSSREFS

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

Sequence in context: A033870 A151901 A157199 * A338220 A242919 A097539

Adjacent sequences: A291348 A291349 A291350 * A291352 A291353 A291354

KEYWORD

nonn,more

AUTHOR

Robert Price, Aug 22 2017

EXTENSIONS

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

STATUS

approved

URL: https://oeis.org/A291351

⇱ A291351 - OEIS