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A239015
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Exponents m such that the decimal expansion of 11^m exhibits its first zero from the right later than any previous exponent.
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7
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
...
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MATHEMATICA
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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
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CROSSREFS
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Cf. A001020, A030706, A020665, A031142, A239008, A239009, A239010, A239011, A239012, A239013, A239014.
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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