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

2, 17, 73, 89, 2475989

Offset: 1

Author

Ctibor O. Zizka, May 01 2019

Keywords

• base
• nonn
• more

Examples

			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.
		

Links

• C. Pomerance and Ch. Spicer, Proof of the Sheldon Conjecture.

Crossrefs

Cf. A000040, A007954, A052382, A097220, A097223, A306766.

Programs

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

Python

from math import prod
from sympy import nextprime
def aupton(terms):
  p, k, t = 2, 1, 0
  while t < terms:
    strp = str(p)
    if '0' not in strp and prod(int(d) for d in strp)%k == 0:
      t += 1; print(p, end=", ")
    p, k = nextprime(p), k+1
aupton(5) # Michael S. Branicky, Feb 17 2021

Extensions

a(5) from Alois P. Heinz, May 01 2019