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

1,1

Comments

These values are only conjectural.

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

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.

Example

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

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

Crossrefs

Cf. A062800, A094776, A259081-A259086.

Sequence in context: A033406 A143759 A020665 * A058907 A045101 A020215

Adjacent sequences: A259081 A259082 A259083 * A259085 A259086 A259087

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 18 2015

Extensions

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

Status

approved