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A307851 Prime numbers prime(k) with a zeroless decimal representation such that (product of decimal digits of prime(k)) / k is an integer. 0
2, 17, 73, 89, 2475989 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
C. Pomerance and Ch. Spicer, Proof of the Sheldon Conjecture.
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A268784 A338088 A155715 * A054568 A338087 A235471
KEYWORD
base,nonn,more
AUTHOR
Ctibor O. Zizka, May 01 2019
EXTENSIONS
a(5) from Alois P. Heinz, May 01 2019
STATUS
approved

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Last modified October 3 22:39 EDT 2023. Contains 365872 sequences. (Running on oeis4.)