A239015 Exponents m such that the decimal expansion of 11^m exhibits its first zero from the right later than any previous exponent.

0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 36, 41, 366, 488, 4357, 69137, 89371, 143907, 542116, 2431369, 5877361, 8966861, 121915452, 123793821, 221788016, 709455085, 1571200127, 2640630712, 6637360862, 64994336645, 74770246842

Offset: 1

Author

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

Keywords

• nonn
• base
• more

Comments

Assume that a zero precedes all decimal expansions. This will take care of those cases in A001020.

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.

Examples

			Illustration of initial term, with the 0 enclosed in parentheses:
n, position of 0, 11^a(n)
1, 2, (0)1
2, 3, (0)11
3, 4, (0)121
4, 5, (0)1331
5, 6, (0)14641
6, 7, (0)1771561
7, 8, (0)19487171
8, 9, (0)214358881
9, 10, (0)2357947691
10, 11, (0)3138428376721
11, 12, (0)34522712143931
12, 13, (0)379749833583241
13, 14, (0)4177248169415651
14, 15, (0)45949729863572161
15, 16, (0)5559917313492231481
16, 17, 3091268053287(0)672635673352936887453361
...
- _N. J. A. Sloane_, Jan 16 2020
		

Crossrefs

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

Programs

Mathematica

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

Extensions

a(28)-a(34) from Bert Dobbelaere, Jan 22 2019

a(35)-a(36) from Chai Wah Wu, Jan 16 2020