A239009 Exponents m such that the decimal expansion of 4^m exhibits its first zero from the right later than any previous exponent.

0, 2, 4, 7, 9, 12, 14, 16, 17, 23, 34, 36, 38, 43, 77, 88, 216, 350, 979, 24186, 28678, 134759, 205829, 374627, 2200364, 16625243, 29451854, 162613199, 8078176309, 9252290259, 17556077280, 49718535383, 51616746477, 54585993918

Offset: 1

Author

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

Keywords

• nonn
• base
• more

Comments

Assume that a zero precedes all decimal expansions. This will take care of those cases in A030701.

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.

Not just twice A031142, although {16625243, 29451854, 162613199, 9252290259, 51616746477, 54585993918, 146235898847, 1360645542292} are possible candidates.

Location of first zeros (from the right) of terms: 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 23, 24, 27, 30, 39, 53, 58, 94, 113, 120, 121, 122, 139, 165, 177, 192, 213, 217, 228, 229, 230, 250, 251. - Chai Wah Wu, Jan 08 2020

Crossrefs

Cf. A000302, A030701, A020665, A031142, A239008, A239010, A239011, A239012, A239013, A239014, A239015.

Programs

Mathematica

f[n_] := Position[ Reverse@ Join[{0}, IntegerDigits[ PowerMod[4, 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(28)-a(30) from Bert Dobbelaere, Jan 21 2019

a(31)-a(34) from Chai Wah Wu, Jan 08 2020