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

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A064155.

Sequence in context: A052163 A210363 A054823 * A142369 A190814 A012868

Adjacent sequences: A343698 A343699 A343700 * A343702 A343703 A343704

Keyword

nonn,base

Author

Tanya Khovanova, May 26 2021

Status

approved