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A112388
a(n) is the smallest prime p such that p^n contains every digit.
2
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
MAPLE
f:= proc(n) local k;
k:= 1:
do k:= nextprime(k);
if convert(convert(k^n, base, 10), set) = {$0..9} 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
KEYWORD
base,nonn
AUTHOR
Tanya Khovanova, Dec 05 2005
EXTENSIONS
More terms from Robert G. Wilson v, Dec 06 2005
STATUS
approved