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%I #40 Feb 05 2024 02:06:06
%S 0,16,24,41,220,971,972,8554,42485,42486,271979,1039315,1727602,
%T 6855865,63416789,106892452
%N a(n) is the smallest m for which the decimal representation of 2^m contains n consecutive identical digits.
%C Next term is greater than 20000. - _David Wasserman_, Feb 16 2002
%C a(11) > 250000. - _Robert G. Wilson v_, Oct 21 2010
%C a(15) > 10297974. - _T. D. Noe_, Sep 08 2012
%C a(17) > 107000000. - _Paul Geneau de Lamarlière_, Feb 04 2024
%t a[n_] := Block[{k = 0}, While[ !MemberQ[ Length /@ Split@ IntegerDigits[2^k], n], k++ ]; k]; Table[a[n], {n, 6}] (* _Robert G. Wilson v_, Oct 21 2010 *)
%o (Python)
%o def A045875(n):
%o l, x = [str(d)*n for d in range(10)], 1
%o for m in range(10**9):
%o s = str(x)
%o for k in l:
%o if k in s:
%o return m
%o x *= 2
%o return 'search limit reached'
%o # _Chai Wah Wu_, Dec 17 2014
%Y Cf. A215732 (the digits).
%K base,nonn,hard,more
%O 1,2
%A _Erich Friedman_
%E More terms from _David Wasserman_, Feb 16 2002
%E a(9) and a(10) from _Robert G. Wilson v_, Oct 21 2010
%E a(11)-a(13) added by _T. D. Noe_, Sep 04 2012
%E a(14) added by _T. D. Noe_, Sep 06 2012
%E Definition clarified by _Daran Gill_, Mar 24 2013
%E a(15) from _Bert Dobbelaere_, Feb 25 2019
%E a(16) from _Paul Geneau de Lamarlière_, Feb 04 2024
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