A239015 - OEIS

%I #29 Jan 16 2020 13:03:14

%S 0,1,2,3,4,6,7,8,9,12,13,14,15,16,18,36,41,366,488,4357,69137,89371,

%T 143907,542116,2431369,5877361,8966861,121915452,123793821,221788016,

%U 709455085,1571200127,2640630712,6637360862,64994336645,74770246842

%N Exponents m such that the decimal expansion of 11^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 A001020.

%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_.

%e Illustration of initial term, with the 0 enclosed in parentheses:

%e n, position of 0, 11^a(n)

%e 1, 2, (0)1

%e 2, 3, (0)11

%e 3, 4, (0)121

%e 4, 5, (0)1331

%e 5, 6, (0)14641

%e 6, 7, (0)1771561

%e 7, 8, (0)19487171

%e 8, 9, (0)214358881

%e 9, 10, (0)2357947691

%e 10, 11, (0)3138428376721

%e 11, 12, (0)34522712143931

%e 12, 13, (0)379749833583241

%e 13, 14, (0)4177248169415651

%e 14, 15, (0)45949729863572161

%e 15, 16, (0)5559917313492231481

%e 16, 17, 3091268053287(0)672635673352936887453361

%e ...

%e - _N. J. A. Sloane_, Jan 16 2020

%t f[n_] := Position[ Reverse@ Join[{0}, IntegerDigits[ PowerMod[11, n, 10^500]]], 0, 1, 1][[1, 1]]; k = mx = 0; lst = {}; While[k < 40000001, c = f[k]; If[c > mx, mx = c; AppendTo[ lst, k]; Print@ k]; k++]; lst

%Y Cf. A001020, A030706, A020665, A031142, A239008, A239009, A239010, A239011, A239012, A239013, A239014.

%K nonn,base,more

%O 1,3

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

%E a(28)-a(34) from _Bert Dobbelaere_, Jan 22 2019

%E a(35)-a(36) from _Chai Wah Wu_, Jan 16 2020