

A092762


Least number whose binary representation is not contained in that of n!.


2



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, 31, 21, 36, 15, 15, 35, 42, 41, 35, 33, 22, 45, 22, 36, 46, 50, 41, 37, 33, 21, 40, 38, 31, 66, 33, 60, 45, 51, 42, 42, 60, 35, 38, 63, 65, 75, 75, 39, 71, 36, 75, 67, 74, 67, 68, 78
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OFFSET

1,1


COMMENTS

a(A093710(n)) > n, a(A093711(n)) <= n.
Sum_{n=1..3000} a(n) = 4179226. The average value of a(n)/n > 0.93+ and except for some initial terms, < 212, 0.90 < a(n)/n < 0.95. But there is graphical evidence that this value may increase.  Robert G. Wilson v, Apr 21 2004
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, Apr 21 2004
a(n) >= 3n/2 for n=1, 2, 334, 335, 2693 & 2739.  Robert G. Wilson v, Apr 21 2004
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, Apr 21 2004


LINKS

Table of n, a(n) for n=1..73.


EXAMPLE

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, Apr 21 2004


MATHEMATICA

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, Apr 21 2004 *)


CROSSREFS

Cf. A036603, A007088, A000142, A092601.
Sequence in context: A163382 A343127 A094017 * A017844 A303655 A011156
Adjacent sequences: A092759 A092760 A092761 * A092763 A092764 A092765


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Apr 13 2004


EXTENSIONS

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar


STATUS

approved



