VOOZH about

URL: https://oeis.org/A239008

⇱ A239008 - OEIS

login
A239008
Exponents m such that the decimal expansion of 3^m exhibits its first zero from the right later than any previous exponent.
7
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
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
KEYWORD
nonn,base
EXTENSIONS
a(30)-a(34) from Bert Dobbelaere, Jan 21 2019
a(35)-a(36) from Chai Wah Wu, Jan 06 2020
STATUS
approved