A343701 Prime numbers such that the product of their digits equals twice the number of their digits times the sum of their digits.
347, 743, 15581, 42451, 51581, 54421, 58151, 58511, 81551, 112583, 115823, 118253, 121853, 122443, 123581, 125183, 125813, 128153, 128351, 132851, 135281, 138251, 144223, 152183, 152381, 153281, 158231, 181253, 181523, 185123, 211583, 214243, 215183, 215381, 218513, 218531, 223441, 235181, 235811, 238151, 242413
Offset: 1
Examples
347 is a 3-digit prime number. The product of its digits is 84. The sum of its digits is 14. As 84 = 2*3*14, this number is in the sequence.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A064155.
Programs
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Maple
q:= n-> (l-> mul(i,i=l)=2*nops(l)*add(i,i=l))(convert(n, base, 10)): select(q, [ithprime(j)$j=1..100000])[]; # Alois P. Heinz, May 30 2021
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Mathematica
Select[Range[1000000], PrimeQ[#] && Times@@IntegerDigits[#] == 2 Length[IntegerDigits[#]] Total[IntegerDigits[#]] &] Select[Prime[Range[22000]],Times@@IntegerDigits[#]==2(IntegerLength[#]Total[ IntegerDigits[ #]])&] (* Harvey P. Dale, Jun 30 2023 *)
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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) == 2*len(d)*sum(d) def agen(): 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(), 41))) # Michael S. Branicky, Nov 30 2022