A090840 Smallest prime whose product of digits is 5^n.

11, 5, 11551, 15551, 1551551, 15551551, 1155555151, 1555551551, 11555555551, 1155155555551, 555555515551, 555555555551, 5555555555551, 555155555555551, 51555555551555551, 51555555555555551, 1155555555555555551, 15551555555555555551, 1155515555555555555551

Offset: 0

Author

Robert G. Wilson v, Dec 09 2003

Keywords

• base
• nonn

Examples

			a(4) = 1551551 because its digital product is 5^4, and it is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..998

Crossrefs

Cf. A089365, A088653, A091465, A090841, 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$k, 5$n]))));
      if tAlois P. Heinz, Nov 05 2021

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {18}]; p = 2; Do[q = Log[5, 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(13); a = Map[ FromDigits, Permutations[{1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}]]; 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, 5][n]
    digits = n + 1
    while True:
        for p in mp("1"*(digits-n-1) + "5"*n, digits-1):
            t = int("".join(p) + "1")
            if isprime(t): return t
        digits += 1
print([a(n) for n in range(19)]) # Michael S. Branicky, Nov 05 2021

Extensions

a(17) and beyond from Michael S. Branicky, Nov 05 2021