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

0,7

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.

Links

Table of n, a(n) for n=0..100.

Example

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

Prog

(PARI) (nMax)->my(c=[], cnt(t, s, M)=M=2^#s-1; sum(i=0, #t-#s, vecextract(t, M<<i)==s)); for(n=0, nMax, print1(cnt(c, binary(n))", "); c=concat(c, binary(n)))

Crossrefs

Sequence in context: A364060 A361292 A251690 * A295181 A215573 A163537

Adjacent sequences: A187749 A187750 A187751 * A187753 A187754 A187755

Keyword

nonn

Author

M. F. Hasler, Jan 03 2013

Status

approved