cp's OEIS Frontend

A307851 Prime numbers prime(k) with a zeroless decimal representation such that (product of decimal digits of prime(k)) / k is an integer.

%I A307851 #22 Feb 17 2021 11:46:40
%S A307851 2,17,73,89,2475989
%N A307851 Prime numbers prime(k) with a zeroless decimal representation such that (product of decimal digits of prime(k)) / k is an integer.
%H A307851 C. Pomerance and Ch. Spicer, <a href="https://math.dartmouth.edu/~carlp/sheldon02132019.pdf">Proof of the Sheldon Conjecture</a>.
%e A307851 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 A307851 (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 A307851 (Python)
%o A307851 from math import prod
%o A307851 from sympy import nextprime
%o A307851 def aupton(terms):
%o A307851   p, k, t = 2, 1, 0
%o A307851   while t < terms:
%o A307851     strp = str(p)
%o A307851     if '0' not in strp and prod(int(d) for d in strp)%k == 0:
%o A307851       t += 1; print(p, end=", ")
%o A307851     p, k = nextprime(p), k+1
%o A307851 aupton(5) # _Michael S. Branicky_, Feb 17 2021
%Y A307851 Cf. A000040, A007954, A052382, A097220, A097223, A306766.
%K A307851 base,nonn,more
%O A307851 1,1
%A A307851 _Ctibor O. Zizka_, May 01 2019
%E A307851 a(5) from _Alois P. Heinz_, May 01 2019