A239008 - OEIS

%I #29 Jan 22 2020 14:44:32

%S 0,3,5,7,9,11,13,19,23,24,26,28,31,34,52,65,68,136,237,4947,7648,

%T 42073,50693,52728,395128,2544983,6013333,76350564,160451107,

%U 641814146,5291528429,5856442430,7307126644,11577159988,51444010646,60457925746

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

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

%C 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_.

%C 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

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

%t 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

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

%K nonn,base

%O 1,2

%A _Charles R Greathouse IV_ and _Robert G. Wilson v_, Mar 14 2014

%E a(30)-a(34) from _Bert Dobbelaere_, Jan 21 2019

%E a(35)-a(36) from _Chai Wah Wu_, Jan 06 2020