

A092601


Number of numbers from 1 to n whose binary representation is contained in that of n!.


5



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, 28, 28, 30, 27, 28, 33, 34, 35, 35, 34, 37, 39, 38, 40, 42, 43, 43, 44, 45, 43, 46, 48, 48, 51, 51, 53, 53, 53, 55, 56, 58, 55, 59, 61, 62, 63, 64, 64, 66, 65, 68, 68, 70, 70, 71, 73
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OFFSET

1,2


COMMENTS

a(A093710(n)) = n, a(A093711(n)) < n.
Sequence is not monotonic.


LINKS

Table of n, a(n) for n=1..73.
Index entries for sequences related to factorial numbers.
Index entries for sequences related to binary expansion of n


EXAMPLE

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.


MATHEMATICA

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 *)


CROSSREFS

Cf. A036603, A007088, A000142.
Sequence in context: A039696 A076332 A245092 * A162906 A100476 A248517
Adjacent sequences: A092598 A092599 A092600 * A092602 A092603 A092604


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Apr 08 2004


STATUS

approved



