A092762 Least number whose binary representation is not contained in that of n!.

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

Offset: 1

Author

Reinhard Zumkeller, Apr 13 2004

Keywords

• nonn

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

Examples

			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
		

Crossrefs

Cf. A036603, A007088, A000142, A092601.

Programs

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 *)

Extensions

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