A112388 a(n) is the smallest prime p such that p^n contains every digit.

10123457689, 101723, 5437, 2339, 1009, 257, 139, 173, 83, 67, 31, 29, 37, 17, 17, 47, 19, 7, 5, 23, 23, 5, 11, 11, 17, 5, 5, 5, 5, 11, 5, 11, 11, 5, 5, 7, 5, 7, 3, 5, 5, 7, 7, 7, 3, 7, 3, 3, 5, 5, 5, 5, 3, 7, 7, 5, 3, 7, 5, 3, 3, 3, 3, 3, 3, 5, 3, 2, 3, 2, 3, 3, 3, 3, 5, 3, 3, 3, 2, 3, 5, 2

Offset

1,1

Comments

Conjecture: a(n)=2 for all n>168. Checked up to n = 20000. - Robert Israel, Aug 28 2020

Links

Table of n, a(n) for n=1..82.

Maple

f:= proc(n) local k;
  k:= 1:
  do k:= nextprime(k);
    if ispd(k^n) then return k fi
  od
end proc:
f(1):= 10123457689:
map(f, [$1..100]); # Robert Israel, Aug 28 2020

Mathematica

f[n_] := Block[{k = 1}, While[ Union@IntegerDigits[ Prime[k]^n] != {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, k++ ]; Prime[k]]; Array[f, 82] (* Robert G. Wilson v, Dec 06 2005 *)

Prog

(Python)
from sympy import nextprime
def a(n):
    if n == 1: return 10123457689
    p = 2
    while not(len(set(str(p**n))) == 10): p = nextprime(p)
    return p
print([a(n) for n in range(1, 83)]) # Michael S. Branicky, Jul 04 2021

Crossrefs

Cf. A020666, A020665, A007377, A137214.

Sequence in context: A261458 A296158 A172688 * A225298 A050288 A173051

Adjacent sequences: A112385 A112386 A112387 * A112389 A112390 A112391

Keyword

base,nonn

Author

Tanya Khovanova, Dec 05 2005

Extensions

More terms from Robert G. Wilson v, Dec 06 2005

Status

approved