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%I #27 Jun 02 2019 23:38:38
%S 36,736,8736,48736,948736,2948736,32948736,432948736,3432948736,
%T 53432948736,353432948736,5353432948736,75353432948736,
%U 5075353432948736,15075353432948736,615075353432948736,8615075353432948736,98615075353432948736,8098615075353432948736,38098615075353432948736
%N Numbers k such that 2^k ends in k.
%C There is no term with 15 digits.
%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%F a(n+1) is a suffix of 2^a(n) formed by a nonzero digit followed by a number of zeros and a(n). E.g., a(13)=75353432948736 and 2^a(13) ends with ...15075353432948736, hence a(14)=5075353432948736. - _Max Alekseyev_, Apr 18 2007
%F Can be obtained from A109405 by removing all repeats. - _Max Alekseyev_, May 11 2007
%e 2^36 = 68719476736 which ends in 36.
%t a[1] = 36; a[n_] := a[n] = For[ida = IntegerDigits[a[n-1]]; k = 1, True, k++, idk = IntegerDigits[k]; pm = PowerMod[2, an = FromDigits[Join[idk, ida]], 10^IntegerLength[an]]; If[pm == an, Return[an]]]; Array[a, 20] (* _Jean-François Alcover_, Feb 15 2018 *)
%Y Cf. A121319, A109405, A206636.
%Y The leading digits are listed in A064540.
%Y Digits read backwards form A133612.
%K base,nonn,nice
%O 1,1
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 08 2001
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