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%I #15 Jan 20 2024 16:48:42
%S 11,1013,15619,16369,65519,478271,13824739,67108837,1125899906842573,
%T 72057594037927879,1180591620717411303353,2153693845981967454679177,
%U 12086992684284175368032851,22528399544594441658590663774175461
%N Prime numbers in the triangle of Eulerian numbers.
%H Sean A. Irvine, <a href="/A065050/b065050.txt">Table of n, a(n) for n = 1..18</a>
%e Pairs (n, k) such that Eulerian(n, k) is prime are (4, 2), (10, 2), (8, 4), (14, 2), (16, 2), (12, 3), (15, 3), (26, 2), (50, 2), (56, 2), (70, 2), (51, 3), (27, 9), (72, 3), (116, 2), (87, 3), (183, 3).
%o (PARI) Eulerian(n,k)=sum(j=0,k,(-1)^j*(k-j)^n*binomial(n+1,j));
%o lista(nn) = {my(list=List()); for (n=1, nn, for (k=1, n, if (ispseudoprime(p=Eulerian(n, k)), listput(list, p)););); Vec(Set(list));} \\ _Michel Marcus_, May 25 2022
%Y Cf. A008292, A030196.
%K nonn
%O 1,1
%A _Henry Bottomley_, Nov 06 2001
%E More terms from _Randall L Rathbun_, Jan 21 2002