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URL: https://oeis.org/A343701

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A343701
Prime numbers such that the product of their digits equals twice the number of their digits times the sum of their digits.
1
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
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
KEYWORD
nonn,base
AUTHOR
Tanya Khovanova, May 26 2021
STATUS
approved