%I #22 Feb 17 2021 11:46:40
%S 2,17,73,89,2475989
%N Prime numbers prime(k) with a zeroless decimal representation such that (product of decimal digits of prime(k)) / k is an integer.
%H C. Pomerance and Ch. Spicer, <a href="https://math.dartmouth.edu/~carlp/sheldon02132019.pdf">Proof of the Sheldon Conjecture</a>.
%e For k = 21, prime(21) = 73, product of decimal digits of prime(k) / k = 7 * 3 / 21 = 1 so prime(21) = 73 is in the sequence.
%o (PARI) lista(nn) = {my(ip=0, d); forprime(p=2, nn, ip++; d = digits(p); if (vecmin(d) && !(frac(vecprod(d)/ip)), print1(p, ", ")););} \\ _Michel Marcus_, May 02 2019
%o (Python)
%o from math import prod
%o from sympy import nextprime
%o def aupton(terms):
%o p, k, t = 2, 1, 0
%o while t < terms:
%o strp = str(p)
%o if '0' not in strp and prod(int(d) for d in strp)%k == 0:
%o t += 1; print(p, end=", ")
%o p, k = nextprime(p), k+1
%o aupton(5) # _Michael S. Branicky_, Feb 17 2021
%Y Cf. A000040, A007954, A052382, A097220, A097223, A306766.
%K base,nonn,more
%O 1,1
%A _Ctibor O. Zizka_, May 01 2019
%E a(5) from _Alois P. Heinz_, May 01 2019