Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #8 Jan 07 2013 11:48:29
%S 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,
%T 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,
%U 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
%N Number of times the binary representation of n occurs in the concatenation of the binary representation of all smaller numbers.
%C 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.
%e a(3) = 1 since concatenation of 0,1,2 in binary yields "0110", and 3 = "11"[2] occurs once in this string.
%o (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)))
%K nonn
%O 0,7
%A _M. F. Hasler_, Jan 03 2013