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A187752
Number of times the binary representation of n occurs in the concatenation of the binary representation of all smaller numbers.
1
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.
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 03 2013
STATUS
approved