%I A092762
%S A092762 2,3,4,5,5,7,10,10,7,9,7,5,13,15,15,15,17,17,15,17,18,17,29,21,17,28,20,
%T A092762 31,21,36,15,15,35,42,41,35,33,22,45,22,36,46,50,41,37,33,21,40,38,31,
%U A092762 66,33,60,45,51,42,42,60,35,38,63,65,75,75,39,71,36,75,67,74,67,68,78
%N A092762 Least number k whose binary representation is not contained in that of 
               n!.
%C A092762 a(A093710(n)) > n, a(A093711(n)) <= n.
%C A092762 The sum_{n=1..3000} a(n) = 4179226. The average value of a(n)/n -> 0.93+ 
               and except for some initial terms, <212, .90 < a(n)/n < .95. But 
               there is graphical evidence that this value may increase. - Robert 
               G. Wilson v (rgwv(AT)rgwv.com), Apr 21 2004
%C A092762 a(n)=n only for 5, 13, 15, 17, 513, 517, 1041, 1538, 2138, n <= 2500. 
               a(n)=n+1 for n=1, 2, 3, 4, 6, 14, 134, 137, 155, 169, 216, 313, 530, 
               1035 & 2402. - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 21 2004
%C A092762 a(n)>=3n/2 for n=1, 2, 334, 335, 2693 & 2739. - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Apr 21 2004
%C A092762 a(n)<=n/2 for n=12, 31, 32, 47, 122, 142, 152, 188, 303, 378, 443, 548, 
               598, 1319, 1354, 1420, 2127, 2137, 2223, 2230, 2368, 2433, 2571. 
               - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 21 2004
%e A092762 a(7)=10 because 7! = 1001110110000_b and 1_b, 10_b, 11_b, 100_b, 101_b, 
               110_b, 111_b, 1000_b & 1001_b are substrings, but 10_d = 1010_b is 
               not a substring. - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 21 
               2004
%t A092762 f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; g[n_] := g[n] = 
               Block[{k = 1, s = f[n! ]}, While[ StringPosition[ s, f[k]] != {}, 
               k++ ]; k]; Table[ g[n], {n, 75}] - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Apr 21 2004
%Y A092762 Cf. A036603, A007088, A000142, A092601.
%Y A092762 Sequence in context: A031218 A163382 A094017 this_sequence A017844 A011156 
               A037849
%Y A092762 Adjacent sequences: A092759 A092760 A092761 this_sequence A092763 A092764 
               A092765
%K A092762 nonn
%O A092762 1,1
%A A092762 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 13 2004
%E A092762 Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2008 at 
               the suggestion of R. J. Mathar