A064155 Primes whose product of digits equals the number of digits times the sum of digits.
2, 3, 5, 7, 167, 523, 617, 761, 1427, 2417, 2741, 4127, 4217, 4271, 4721, 126241, 126421, 146221, 212461, 216421, 221461, 224611, 226141, 241261, 242161, 246121, 261241, 262411, 264211, 421621, 426211, 621241, 642121, 642211, 1111457, 1111547, 1115417, 1117451
Offset: 1
Examples
167 belongs to the sequence because 1*6*7 = 42 and 3*(1+6+7) = 42.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..100 from Harry J. Smith)
Crossrefs
Primes in A064154.
Programs
-
Mathematica
Select[Prime@Range@1000000, Plus@@(i=IntegerDigits@#)*Length@i == Times@@i&] (*Hans Rudolf Widmer, Jun 13 2024*)
-
PARI
isok(k)={ if(isprime(k), my(d=digits(k)); vecprod(d)==#d * vecsum(d), 0) } \\ Harry J. Smith, Sep 09 2009 -
Python
from math import prod from sympy import isprime from sympy.utilities.iterables import multiset_permutations as mp from itertools import count, islice, combinations_with_replacement as mc def c(s): d = list(map(int, s)) return prod(d) == len(d)*sum(d) def agen(): yield from (2, 3, 5, 7) for d in count(2): okset = set() for cand in ("".join(m) for m in mc("987654321", d)): if c(cand): for p in mp(cand, d): t = int("".join(p)) if isprime(t): okset.add(t) yield from sorted(okset) print(list(islice(agen(), 38))) # Michael S. Branicky, Nov 30 2022
Extensions
Name edited by Andrew Howroyd, Dec 05 2024
Comments