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%I #24 Jan 20 2020 01:34:31
%S 0,2,3,5,6,9,11,15,17,18,25,26,30,33,57,58,153,1839,3290,4081,16431,
%T 577839,2190974,15167023,23155442,24477994,36290003,53687441,62497567,
%U 181850218,790111167,872257561,4531889178,26964400609,32626158305,268600630073
%N Exponents m such that the decimal expansion of 5^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 A008839.
%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 C. Wechsler_ and _Franklin T. Adams-Watters_.
%C Highest position known is 232th digit from the right for a(33). - _Bert Dobbelaere_, Jan 21 2019
%t f[n_] := Position[ Reverse@ Join[{0}, IntegerDigits[ PowerMod[5, n, 10^500]]], 0, 1, 1][[1, 1]]; k = mx = 0; lst = {}; While[k < 100000001, c = f[k]; If[c > mx, mx = c; AppendTo[ lst, k]; Print@ k]; k++]; lst
%Y Cf. A000351, A008839, A020665, A031142, A239008, A239009, 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(33) from _Bert Dobbelaere_, Jan 21 2019
%E a(34)-a(36) from _Chai Wah Wu_, Jan 18 2020
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