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

1,2

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

Links

Table of n, a(n) for n=1..34.

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

Crossrefs

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

Sequence in context: A027904 A193600 A190429 * A287074 A304501 A283964

Adjacent sequences: A239006 A239007 A239008 * A239010 A239011 A239012

Keyword

nonn,base,more

Author

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

Extensions

a(28)-a(30) from Bert Dobbelaere, Jan 21 2019

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

Status

approved