A239008 Exponents m such that the decimal expansion of 3^m exhibits its first zero from the right later than any previous exponent.

0, 3, 5, 7, 9, 11, 13, 19, 23, 24, 26, 28, 31, 34, 52, 65, 68, 136, 237, 4947, 7648, 42073, 50693, 52728, 395128, 2544983, 6013333, 76350564, 160451107, 641814146, 5291528429, 5856442430, 7307126644, 11577159988, 51444010646, 60457925746

Offset

1,2

Comments

Assume that a zero precedes all decimal expansions. This will take care of those cases in A030700.

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 Wechsler and Franklin T. Adams-Watters.

Location of first zeros (from the right) of terms: 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 18, 21, 22, 34, 57, 82, 84, 99, 103, 104, 139, 144, 151, 166, 169, 173, 202, 204, 205, 220, 230, 233, 236. - Chai Wah Wu, Jan 06 2020

Links

Table of n, a(n) for n=1..36.

Example

Obviously a(1) is 0. a(2) is 3 since this is the first exponent which yields a two-digit (nonzero) power of three.

Mathematica

f[n_] := Position[ Reverse@ Join[{0}, IntegerDigits[ PowerMod[3, n, 10^500]]], 0, 1, 1][[1, 1]]; k = 1; mx = 0; lst = {}; While[k < 200000001, c = f[k]; If[c > mx, mx = c; AppendTo[ lst, k]; Print@ k]; k++]; lst

Crossrefs

Cf. A000244, A030700, A020665, A031142, A239009, A239010, A239011, A239012, A239013, A239014, A239015.

Sequence in context: A172095 A309361 A133854 * A291343 A030155 A143448

Adjacent sequences: A239005 A239006 A239007 * A239009 A239010 A239011

Keyword

nonn,base

Author

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

Extensions

a(30)-a(34) from Bert Dobbelaere, Jan 21 2019

a(35)-a(36) from Chai Wah Wu, Jan 06 2020

Status

approved