A090841 Smallest prime whose product of digits is 7^n.

11, 7, 11177, 1777, 71777, 1777717, 1177717771, 77777177, 7177717777, 1777777777, 71777777777, 1717777777777, 7177777777777, 17777777777777, 17177777777777717, 7717777777777777, 1177777777177777777, 1777777777777777177, 7777177777777777777

Offset: 0

Author

Robert G. Wilson v, Dec 09 2003

Keywords

• base
• nonn

Examples

			a(6) = 1177717771 because its digital product is 7^6, and it is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..999

Crossrefs

Cf. A089365, A088653, A090840, A091465, A089298.

Programs

Maple

a:= proc(n) local k, t; for k from 0 do t:= min(select(isprime,
      map(x-> parse(cat(x[])), combinat[permute]([1$k, 7$n]))));
      if tAlois P. Heinz, Nov 07 2021

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {18}]; p = 2; Do[q = Log[7, Times @@ IntegerDigits[p]]; If[q != 0 && IntegerQ[q] && a[[q]] == 0, a[[q]] = p; Print[q, " = ", p]]; p = NextPrim[p], {n, 1, 10^9}]
For a(8); a = Map[ FromDigits, Permutations[{1, 1, 7, 7, 7, 7, 7, 7, 7, 7}]]; Min[ Select[a, PrimeQ[ # ] &]]

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations as mp
def a(n):
    if n < 2: return [11, 7][n]
    digits = n
    while True:
        for p in mp("1"*(digits-n) + "7"*n, digits):
            t = int("".join(p))
            if isprime(t): return t
        digits += 1
print([a(n) for n in range(19)]) # Michael S. Branicky, Nov 07 2021

Extensions

a(17) and beyond from Michael S. Branicky, Nov 07 2021