A265200 -id:A265200 - cp's OEIS frontend

A265378 Numbers n such that n!3 + 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

4, 8, 10, 11, 14, 17, 20, 22, 29, 32, 44, 56, 61, 173, 202, 211, 215, 241, 388, 410, 416, 569, 583, 680, 823, 964, 1271, 1732, 2309, 2335, 2404, 2765, 3019, 3047, 4670, 5209, 6320, 6817, 7531, 9923, 11243, 14912, 17969, 21193, 28940

Offset: 1

Robert Price, Dec 07 2015

Corresponding primes are: 19687, 19763, 19963, 20563, 32003, 229123, 4208483, 24364003, 72642189283, ...
a(46) > 50000.
Terms > 61 correspond to probable primes.

			11!3 + 3^9 = 11*8*5*2 + 19683 = 20563 is prime, so 11 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3+19683.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^9] &]

tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^9), print1(n , ", "))) \\ Altug Alkan, Dec 07 2015

A267382 Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

13, 14, 16, 19, 22, 23, 26, 38, 64, 104, 137, 203, 296, 346, 347, 379, 481, 568, 899, 1162, 1603, 2614, 5698, 5846, 9253, 9565, 9848, 10406, 16051, 18377, 23110, 26026, 26120, 28994

Offset: 1

Robert Price, Jan 13 2016

Corresponding primes are: 1453, 10133, 56053, 1104373, 24342133, 2504900213, 3091650738173813, ... .
a(35) > 50000.
Terms > 26 correspond to probable primes.

			13!3 - 3^7 = 13*10*7*4 - 2187 = 1453 is prime, so 13 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-2187.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[13, 50000], PrimeQ[MultiFactorial[#, 3] - 3^7] &]
Select[Range[12,6000],PrimeQ[Times@@Range[#,1,-3]-2187]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Aug 14 2024 *)

A288883 Primes of the form k!3 + 3^7, where k!3 is the triple factorial number (A007661).

Original entry on oeis.org

2267, 2467, 3067, 5827, 60427, 1108747, 4190987, 24346507, 664565853954187, 3091650738178187, 262134882788466690187, 571241722682644258978777268224002187, 1189733928480144370053771930898033195089920002187, 17994728558292550488813850298696914425610240002187

Offset: 1

Robert Price, Jun 18 2017

nonn

Robert Price, Table of n, a(n) for n = 1..18
Henri and Renaud Lifchitz, PRP Records.Search for n!3+3^7.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A007661, A265200.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 3] + 3^7, {i, 0, 100}], PrimeQ[#]&]

a(n) = 2187 + A007661(A265200(n)). - Elmo R. Oliveira, Apr 14 2025

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A265378 Numbers n such that n!3 + 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

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A267382 Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

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A288883 Primes of the form k!3 + 3^7, where k!3 is the triple factorial number (A007661).

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