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%I #12 Dec 09 2014 00:40:57
%S 1,2,3,4,4,6,7,8,8,9,9,9,12,14,14,15,16,17,18,19,20,21,23,23,24,26,26,
%T 28,28,30,27,28,33,34,35,35,34,37,39,38,40,42,43,43,44,45,43,46,48,48,
%U 51,51,53,53,53,55,56,58,55,59,61,62,63,64,64,66,65,68,68,70,70,71,73
%N Number of numbers from 1 to n whose binary representation is contained in that of n!.
%C a(A093710(n)) = n, a(A093711(n)) < n.
%C Sequence is not monotonic.
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e n=5: 5!=1*2*3*4*5=120='1111000': 1='1', 2='10', 3='11' and 4='100' are contained, but not 5='101', therefore a(5)=4.
%t f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; g[n_] := Block[{c = 0, k = 1, s = f[n! ]}, While[k <= n, If[ StringPosition[ s, f[k]] != {}, c++ ]; k++ ]; c]; Table[ g[n], {n, 75}] (* _Robert G. Wilson v_, Apr 21 2004 *)
%Y Cf. A036603, A007088, A000142.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Apr 08 2004
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