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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Corresponding primes are 6563, 6571, 6841, 2504908961, 17961239302561, 81359229958561, 664565853958561, ...
Terms > 68 correspond to probable primes.
a(36) > 50000.
LINKS
Henri & Renaud Lifchitz, PRP Records. Search for n!3+3^8
OpenPFGW Project, Primality Tester
EXAMPLE
10!3 + 3^4 = 10*7*4*1 + 6561 = 6841 is prime, so 10 is in the sequence.
MATHEMATICA
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 *)
PROG
(PARI) is(n)=ispseudoprime(n!!! + 3^8) \\ Anders Hellström, Nov 27 2015
(PARI) 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
CROSSREFS
Sequence in context: A297860 A002094 A212709 * A354832 A115725 A305577
KEYWORD
nonn,more
AUTHOR
Robert Price, Nov 26 2015
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)