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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 Table of n, a(n) for n=1..5. 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 Cf. A000040, A007954, A052382, A097220, A097223, A306766. Sequence in context: A268784 A338088 A155715 * A054568 A338087 A235471 Adjacent sequences: A307848 A307849 A307850 * A307852 A307853 A307854 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.)