A242994 -id:A242994 - cp's OEIS frontend

A291350 Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

9, 11, 13, 17, 19, 21, 29, 31, 33, 35, 67, 103, 111, 129, 179, 355, 713, 799, 921, 1013, 1389, 1543, 2097, 2287, 3657, 4115, 7031, 10689, 11715, 16401, 16893, 19497, 29737, 35615

Offset: 1

Robert Price, Aug 22 2017

Corresponding primes are: 557, 743, 1097, 10457, 66347, 209357, 151413137, ...
a(35) > 10^5.
Terms > 35 correspond to probable primes.

			11!4 + 2^9 = 11*7*3*1 + 512 = 743 is prime, so 11 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+512.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

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

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^9] &]

A291351 Numbers k such that k!4 + 2^10 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

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

Offset: 1

Robert Price, Aug 22 2017

Corresponding primes are: 1069, 1609, 1515229, 40884559, 4996617649, ...
a(37) > 10^5.
Terms > 33 correspond to probable primes.

			13!4 + 2^10 = 13*9*5*1 + 1024 = 1609 is prime, so 13 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!4+1024.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

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

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 *)

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

A374901 Numbers k such that k!^2 + ((k - 1)!^2) + 1 is prime.

Original entry on oeis.org

1, 3, 4, 6, 10, 11, 118, 271, 288, 441, 457, 2931, 5527, 6984, 9998, 10395, 13703

Offset: 1

Arsen Vardanyan, Jul 31 2024

a(18) > 15000 - Karl-Heinz Hofmann, Aug 23 2024

			4 is a term, because 4!^2 + 3!^2 + 1 = 576 + 36 + 1 = 613 is a prime number.

Cf. A000142, A055490, A358805, A358878, A359180, A080778, A243078, A242994

PARI
```
is(k) = isprime((k!^2)+((k-1)!)^2+1);
```

from itertools import count, islice
from sympy import isprime
def A374901_gen(): # generator of terms
    f = 1
    for k in count(1):
        if isprime((k**2+1)*f+1):
            yield k
        f *= k**2
A374901_list = list(islice(A374901_gen(),10)) # Chai Wah Wu, Oct 02 2024

a(12)-a(14) from Michael S. Branicky, Aug 01 2024

a(15)-a(17) from Karl-Heinz Hofmann, Aug 23 2024

cp's OEIS Frontend

A291350 Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

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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).

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A374901 Numbers k such that k!^2 + ((k - 1)!^2) + 1 is prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Python

Extensions