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%I #66 May 20 2022 23:05:09
%S 2,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,1,1,0,1,1,1,1,0,0,0,0,
%T 1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,1,1,
%U 0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0
%N Lower limit of backward value of 2^n and n!.
%C For n!, omitting the trailing sequence zeros. - _Simon Plouffe_, Mar 05 2017
%C The terms are deduced from sequence A023415.
%C The sum of constants in A145679 and A023415 is conjectured to be 11 exactly.
%o (Python)
%o # lower limit of backward value of 2^n
%o a,i=2,0; x=a
%o while 1:
%o i+=1; print x, ',' ,
%o if a%2**(i+1) == 0: x=0
%o else: x=1; a+=10**i
%o # _Cezary Glowacz_, Mar 11 2017
%Y Cf. A000079, A004154, A023415, A158624, A158625.
%K nonn,base
%O 1,1
%A _Simon Plouffe_, Mar 23 2009
%E More terms from _Cezary Glowacz_, Feb 26 2017
%E More terms from _Jinyuan Wang_, Mar 01 2020
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