A243078 -id:A243078 - cp's OEIS frontend

A249400 Numbers n such that n!3 + 3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 19, 20, 26, 28, 29, 32, 41, 56, 61, 77, 100, 169, 181, 205, 338, 347, 955, 1952, 2197, 2428, 2960, 3430, 4618, 7478, 8209, 8422, 9235, 11107, 13481, 18194, 19229, 29854, 46532

Offset: 1

Robert Price, Oct 27 2014

Large terms correspond to probable primes.

a(44) > 50000.

			11!3+3 = 11*8*5*2+3 = 883 is prime, so 11 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-27
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester
Eric Weisstein's World of Mathematics, Multifactorial

Cf. A007661, A037082, A084438, A243078.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] + 3], AppendTo[lst, n]], {n, 100}];lst

A264867 Numbers n such that n!3 + 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

2, 5, 10, 26, 34, 35, 37, 59, 68, 76, 104, 106, 188, 193, 242, 278, 287, 290, 572, 772, 773, 1304, 2384, 2716, 3715, 4562, 6706, 11489, 11711, 21602, 24295, 24775, 27224, 29935, 37856

Offset: 1

Robert Price, Nov 26 2015

Corresponding primes are 6563, 6571, 6841, 2504908961, 17961239302561, 81359229958561, 664565853958561, ...
Terms > 68 correspond to probable primes.
a(36) > 50000.

			10!3 + 3^4 = 10*7*4*1 + 6561 = 6841 is prime, so 10 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3+3^8
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A243078.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^8] &]
Select[Range[800],PrimeQ[6561+Times@@Range[#,1,-3]]&] (* Harvey P. Dale, Mar 08 2023 *)

is(n)=ispseudoprime(n!!! + 3^8) \\ Anders Hellström, Nov 27 2015

tf(n) = prod(i=0,(n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^8), print1(n , ", "))) \\  Altug Alkan, Dec 03 2015

A289817 Primes of the form k!3-9, where k!3 is the triple factorial number (A007661).

Original entry on oeis.org

19, 71, 271, 3631, 58231, 209431, 4188791, 96342391, 17041023991, 72642169591, 2324549427191, 1143053268797439991, 52580450364682239991, 262134882788466687991, 694657439389436723199991, 38900816605808456499199991, 2295148179742698933452799991

Offset: 1

Robert Price, Jul 12 2017

nonn

Robert Price, Table of n, a(n) for n = 1..24
Henri & Renaud Lifchitz, PRP Records.Search for n!3-9.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A243078.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 3] - 9, {i, 5, 100}], PrimeQ[#]&]

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

A249400 Numbers n such that n!3 + 3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

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A264867 Numbers n such that n!3 + 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

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A289817 Primes of the form k!3-9, where k!3 is the triple factorial number (A007661).

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Author

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Mathematica

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

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