A259084 a(n) = largest k such that the decimal representation of prime(n)^k does not contain the digit 0.

86, 68, 58, 35, 41, 14, 27, 44, 10, 14, 16, 16, 9, 10, 8, 7, 14, 16, 14, 8, 6, 9, 4, 23, 8, 0, 14, 10, 12, 10, 6, 14, 5, 8, 5, 13, 7, 16, 7, 17, 6, 3, 9, 9, 16, 7, 12, 11, 4, 13, 7, 16, 8, 9, 3, 10, 4, 9, 6, 4, 5, 13, 3, 12, 7, 9, 6, 8, 4, 39, 13, 12, 10, 4

Offset: 1

Author

N. J. A. Sloane, Jun 18 2015

Keywords

• nonn
• base

Comments

These values are only conjectural.

a(n) = 0 if prime(n) is in A062800. - Robert Israel, Jun 19 2015

Examples

			a(1)=86 because 2^86 = 77371252455336267181195264 is conjectured to be the highest power of 2 that doesn't contain the digit 0.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..500
• Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

Crossrefs

Cf. A062800, A094776, A259081-A259086.

Programs

Maple

N:= 100: K:= 100:  # to get a(1) to a(N), searching up to k = K
for n from 1 to N do
  p:= ithprime(n);
  A[n]:= 0;
  for k from 1 to K do
    if not has(convert(p^k,base,10),0) then
       A[n]:= k
    fi
  od
od:
seq(A[n],n=1..N); # Robert Israel, Jun 19 2015

Extensions

a(14)-a(57) from Hiroaki Yamanouchi, Jun 19 2015