A187752 Number of times the binary representation of n occurs in the concatenation of the binary representation of all smaller numbers.

0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 3, 2, 3, 4, 3, 0, 1, 1, 2, 1, 2, 0, 6, 2, 3, 3, 5, 5, 4, 6, 4, 0, 1, 1, 2, 0, 3, 2, 3, 1, 3, 1, 4, 1, 3, 3, 8, 2, 3, 4, 4, 3, 5, 3, 8, 5, 5, 5, 6, 8, 5, 8, 5, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 4, 1, 5, 3, 4, 1, 3, 2, 5, 2, 4, 2, 6, 1, 4, 3, 6, 2, 6, 4, 10, 2, 3, 4, 4, 3

Offset: 0

Author

M. F. Hasler, Jan 03 2013

Keywords

• nonn

Comments

Related to "early bird" (decimal: A116700, binary: A161373) and Hannah Rollman's numbers (cf. A048991, A048992 for decimal; A118248 and A118247-A118251 for binary versions). The latter would correspond to a variant of this sequence which has indices of nonzero terms omitted from the concatenation.

Examples

			a(3) = 1 since concatenation of 0,1,2 in binary yields "0110", and 3 = "11"[2] occurs once in this string.
		

Programs

PARI

(nMax)->my(c=[],cnt(t,s,M)=M=2^#s-1;sum(i=0,#t-#s,vecextract(t,M<