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A121319 a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits (cf. A113627).

%I A121319 #21 Jun 10 2018 20:25:13
%S A121319 14,36,736,8736,48736,948736,2948736,32948736,432948736,3432948736,
%T A121319 53432948736,353432948736,5353432948736,75353432948736,
%U A121319 1075353432948736,5075353432948736,15075353432948736,615075353432948736,8615075353432948736,98615075353432948736
%N A121319 a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits (cf. A113627).
%H A121319 Jon E. Schoenfield, <a href="/A121319/b121319.txt">Table of n, a(n) for n = 1..80</a>
%H A121319 Jon E. Schoenfield, <a href="/A121319/a121319.txt">Excel program</a>
%F A121319 If A109405(n) has n digits, a(n) = A109405(n), otherwise a(n) = A109405(n) + 10^n. - _Max Alekseyev_, May 05 2007
%e A121319 2^14 = 16384 and 14 end with the same single digit 4, thus a(1) = 14.
%t A121319 f[n_] := Block[{k = If[n == 1, 2, 10], m = 10^n}, While[ PowerMod[2, k, m] != Mod[k, m], k += 2]; k]; Do[ Print@f@n, {n, 9}] (* _Robert G. Wilson v_ *)
%o A121319 (PARI) A121319(n) = { local(k,tn); tn=10^n ; forstep(k=2,1000000000,2, if ( k % tn == (2^k) % tn, return(k) ; ) ; ) ; return(0) ; } { for(n = 1,13, print( A121319(n)) ; ) ; } \\ _R. J. Mathar_, Aug 27 2006
%Y A121319 Cf. A007185, A016090, A003226, A035383, A064540, A064541, A109405.
%K A121319 nonn,base
%O A121319 1,1
%A A121319 _Tanya Khovanova_, Aug 25 2006
%E A121319 a(6)-a(9) from _Robert G. Wilson v_ and _Jon E. Schoenfield_, Aug 26 2006
%E A121319 a(10) from _Robert G. Wilson v_, Sep 26 2006
%E A121319 a(11)-a(16) from _Alexander Adamchuk_, Jan 28 2007
%E A121319 a(16) corrected by _Max Alekseyev_, Apr 12 2007