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A291122 Numbers k such that k!4 + 2^2 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662). 1
0, 1, 3, 15, 17, 19, 23, 25, 27, 29, 35, 49, 63, 79, 87, 105, 139, 319, 339, 409, 441, 477, 1023, 1107, 1517, 1557, 1625, 4215, 5297, 6291, 6499, 7357, 11639, 12963, 13989, 15825, 19993, 20535, 35391, 58483, 69247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Corresponding primes are: 5, 5, 7, 3469, 9949, 65839, 1514209, 5221129, 40883539, ...

a(42) > 10^5.

Terms > 35 correspond to probable primes.

LINKS

Table of n, a(n) for n=1..41.

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

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

EXAMPLE

15!4 + 2^2 = 15*11*7*3*1 + 4 = 3469 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] + 2^2] &]

CROSSREFS

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

Sequence in context: A043060 A029476 A154317 * A323033 A080705 A032921

Adjacent sequences:  A291119 A291120 A291121 * A291123 A291124 A291125

KEYWORD

nonn,more

AUTHOR

Robert Price, Aug 17 2017

EXTENSIONS

a(40)-a(41) from Robert Price, Sep 25 2019

STATUS

approved

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Last modified October 25 21:15 EDT 2021. Contains 348256 sequences. (Running on oeis4.)