A347196 - OEIS

%I #35 Oct 09 2021 15:55:57

%S 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,

%T 1,12,13,130,49,88,16,67,31,20,3,56,22,24,8,6,38,28,84,50,17,32,4,70,

%U 9,39,36,90,33,0,40,110,11,12,43,322,129,224,48,175,87,53,15

%N 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) + ... ).

%C 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.

%H Thomas Scheuerle, <a href="/A347196/b347196.txt">Table of n, a(n) for n = 0..5000</a>

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

%e pos:0,1,2,3,4,5,6,7,8,9,...

%e c:  0|1|0,1|1,1|0,0,1|1,0,1...

%e     0                           a(0) = 0

%e     . 1                         a(1) = 1

%e     0 1                         a(2) = 0

%e     . . . 1 1                   a(3) = 3

%e     . . . . . . 0 0 1           a(4) = 6

%e     . 1 0 1                     a(5) = 1

%e     . . 0 1 1                   a(6) = 2

%o (MATLAB)

%o function a = A347196( max_n)

%o     c = 0; a = 0;

%o     for n = 1:max_n

%o         b = bitget(n,1:64);

%o         c = [c b(1:find(b == 1, 1, 'last' ))];

%o     end

%o     for n = 1:max_n

%o         b = bitget(n,1:64);

%o         word = b(1:find(b == 1, 1, 'last' ));

%o         pos = strfind(c, word);

%o         a(n+1) = pos(1)-1;

%o     end

%o end

%Y Cf. A030304, A030308, A030311, A070939.

%K nonn,base,easy,look

%O 0,4

%A _Thomas Scheuerle_, Aug 22 2021