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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

%I

%S 2,5,10,26,34,35,37,59,68,76,104,106,188,193,242,278,287,290,572,772,

%T 773,1304,2384,2716,3715,4562,6706,11489,11711,21602,24295,24775,

%U 27224,29935,37856

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

%C Corresponding primes are 6563, 6571, 6841, 2504908961, 17961239302561, 81359229958561, 664565853958561, ...

%C Terms > 68 correspond to probable primes.

%C a(36) > 50000.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+6561&amp;action=Search">PRP Records. Search for n!3+3^8</a>

%H Joe McLean, <a href="http://web.archive.org/web/20091027034731/http://uk.geocities.com/nassarawa%40btinternet.com/probprim2.htm">Interesting Sources of Probable Primes</a>

%H OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>

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

%t MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];

%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^8] &]

%o (PARI) is(n)=ispseudoprime(n!!! + 3^8) \\ _Anders Hellström_, Nov 27 2015

%o (PARI) tf(n) = prod(i=0,(n-1)\3, n-3*i);

%o for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^8), print1(n , ", "))) \\ _Altug Alkan_, Dec 03 2015

%Y Cf. A007661, A037082, A084438, A243078.

%K nonn,more

%O 1,1

%A _Robert Price_, Nov 26 2015

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)