A239010 Exponents m such that the decimal expansion of 5^m exhibits its first zero from the right later than any previous exponent.

0, 2, 3, 5, 6, 9, 11, 15, 17, 18, 25, 26, 30, 33, 57, 58, 153, 1839, 3290, 4081, 16431, 577839, 2190974, 15167023, 23155442, 24477994, 36290003, 53687441, 62497567, 181850218, 790111167, 872257561, 4531889178, 26964400609, 32626158305, 268600630073

Offset: 1

Author

Charles R Greathouse IV and Robert G. Wilson v, Mar 14 2014

Keywords

• nonn
• base

Comments

Assume that a zero precedes all decimal expansions. This will take care of those cases in A008839.

Inspired by the seqfan list discussion Re: "possible sequence", beginning with David Wilson 7:57 PM Mar 06 2014 and continued by M. F. Hasler, Allan C. Wechsler and Franklin T. Adams-Watters.

Highest position known is 232th digit from the right for a(33). - Bert Dobbelaere, Jan 21 2019

Crossrefs

Cf. A000351, A008839, A020665, A031142, A239008, A239009, A239011, A239012, A239013, A239014, A239015.

Programs

Mathematica

f[n_] := Position[ Reverse@ Join[{0}, IntegerDigits[ PowerMod[5, n, 10^500]]], 0, 1, 1][[1, 1]]; k = mx = 0; lst = {}; While[k < 100000001, c = f[k]; If[c > mx, mx = c; AppendTo[ lst, k]; Print@ k]; k++]; lst

Extensions

a(30)-a(33) from Bert Dobbelaere, Jan 21 2019

a(34)-a(36) from Chai Wah Wu, Jan 18 2020