A347196 Let c(k) be the infinite binary string 010111001... (A030308), the concatenation of reverse order integer binary words ( 0;1;01;11;001;101;... ). a(n) is the bit index k of the first occurrence of the reverse order binary word of n ( n = 2^0*c(a(n)) + 2^1*c(a(n)+1) + ... ).
0, 1, 0, 3, 6, 1, 2, 3, 18, 5, 0, 8, 6, 1, 2, 13, 50, 17, 32, 4, 23, 9, 7, 29, 18, 5, 0, 37, 34, 1, 12, 13, 130, 49, 88, 16, 67, 31, 20, 3, 56, 22, 24, 8, 6, 38, 28, 84, 50, 17, 32, 4, 70, 9, 39, 36, 90, 33, 0, 40, 110, 11, 12, 43, 322, 129, 224, 48, 175, 87, 53, 15
Offset: 0
Examples
pos:0,1,2,3,4,5,6,7,8,9,...
c: 0|1|0,1|1,1|0,0,1|1,0,1...
0 a(0) = 0
. 1 a(1) = 1
0 1 a(2) = 0
. . . 1 1 a(3) = 3
. . . . . . 0 0 1 a(4) = 6
. 1 0 1 a(5) = 1
. . 0 1 1 a(6) = 2
Links
- Thomas Scheuerle, Table of n, a(n) for n = 0..5000
Programs
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MATLAB
function a = A347196( max_n) c = 0; a = 0; for n = 1:max_n b = bitget(n,1:64); c = [c b(1:find(b == 1, 1, 'last' ))]; end for n = 1:max_n b = bitget(n,1:64); word = b(1:find(b == 1, 1, 'last' )); pos = strfind(c, word); a(n+1) = pos(1)-1; end end
Formula
a(n) <= Sum_{k=0..n} A070939(k).
Comments