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

0,4

Comments

It is not surprising to see dyadic self-similarity in the graph of this sequence. For example the graph of a(0..2^9) looks like a rescaled version of a(0..2^8). Each of these intervals reminds a bit of particle traces in a cloud chamber.

Links

Thomas Scheuerle, Table of n, a(n) for n = 0..5000

Formula

a(n) <= Sum_{k=0..n} A070939(k).

Example

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

Prog

(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

Crossrefs

Cf. A030304, A030308, A030311, A070939.

Sequence in context: A368569 A032660 A102257 * A091425 A369883 A205005

Adjacent sequences: A347193 A347194 A347195 * A347197 A347198 A347199

Keyword

nonn,base,easy,look

Author

Thomas Scheuerle, Aug 22 2021

Status

approved