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

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..100 from Harry J. Smith)

Example

167 belongs to the sequence because 1*6*7 = 42 and 3*(1+6+7) = 42.

Mathematica

Select[Prime@Range@1000000, Plus@@(i=IntegerDigits@#)*Length@i == Times@@i&] (*Hans Rudolf Widmer, Jun 13 2024*)

Prog

(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

Crossrefs

Primes in A064154.

Sequence in context: A281021 A230046 A098463 * A230047 A230042 A230045

Adjacent sequences: A064152 A064153 A064154 * A064156 A064157 A064158

Keyword

easy,nonn,base

Author

Felice Russo, Sep 14 2001

Extensions

Name edited by Andrew Howroyd, Dec 05 2024

Status

approved