A155891 Least positive integer such that a(n)! starts with n, both written in binary.

1, 2, 3, 7, 6, 3, 5, 20, 7, 14, 6, 4, 10, 12, 5, 20, 27, 50, 7, 14, 23, 6, 13, 4, 25, 30, 10, 12, 51, 5, 63, 24, 20, 36, 27, 50, 59, 11, 7, 14, 26, 75, 23, 9, 6, 13, 49, 71, 144, 31, 25, 30, 199, 19, 10, 46, 12, 51, 83, 5, 28, 73, 63, 62, 24, 54, 20, 36, 67, 27, 40, 74, 50, 59, 124

Offset: 1

Author

M. F. Hasler, Feb 01 2009

Keywords

• base
• nonn

Examples

			a(7) = 5 since 7 = 111_2 (i.e., written in base 2) and 5! = 1111000_2 is the least factorial to have 111 as its most significant binary digits.
		

Links

• Nick Hobson, Table of n, a(n) for n = 1..16383
• Nick Hobson, C program.

Crossrefs

Cf. A018799, A076219.

Programs

C

See Links section.

PARI

A155891(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=2 )); k}