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A182419 a(0)=0, a(n+1) = (a(n) XOR floor(a(n)/8)) + 1, where XOR is the bitwise exclusive-or operator.

%I A182419 #14 Jun 26 2021 21:42:21
%S A182419 0,1,2,3,4,5,6,7,8,10,12,14,16,19,18,17,20,23,22,21,24,28,32,37,34,39,
%T A182419 36,33,38,35,40,46,44,42,48,55,50,53,52,51,54,49,56,64,73,65,74,68,77,
%U A182419 69,78,72,66,75,67,76,70,79,71,80,91,81,92,88,84,95
%N A182419 a(0)=0, a(n+1) = (a(n) XOR floor(a(n)/8)) + 1, where XOR is the bitwise exclusive-or operator.
%C A182419 Para-random values on each interval (2^k,2^(k+1)-1), then jump to the next interval (2^(k+1),2^(k+2)-1).
%C A182419 Floor(100*log_2(indices of 2^x)):
%C A182419 0, 100, 200, 300, 358, 445, 542, 642, 708, 752, 898, 985, 1042, 1176, 1245, 1319, 1462, 1521, 1588, 1714, 1809, 1906, 1963, 2049, 2149, 2260, 2402, 2481, 2553, 2657, 2770, 2835, 2929, 3004, 3164, 3281, 3346, 3472, 3557, 3646, 3694, 3801, 3935, 4027, 4135, 4214, 4294, 4415
%C A182419 Given a(n), the previous term a(n-1) can be unambiguously reconstructed as in the C program.
%C A182419 As n -> infinity, a(n) -> infinity.
%o A182419 (C)
%o A182419 #include <stdio.h>
%o A182419 int main(int argc, char **argv) {
%o A182419   unsigned long long a=0;
%o A182419   for (int j=0; j<1000; ++j) {
%o A182419     printf("%llu, ", a);
%o A182419     a = (a^(a/8)) + 1;
%o A182419   }
%o A182419   return 0;     // indices of 2^x: see C program of A182310.
%o A182419 }               // from _Alex Ratushnyak_, Apr 27 2012
%o A182419 (PARI)
%o A182419 N=100; v=vector(N);
%o A182419 for (n=1, N-1, v[n+1] = bitxor( v[n], v[n] \ 8 ) + 1 );
%o A182419 v /* show terms */
%o A182419 /* _Joerg Arndt_, Apr 28 2012 */
%Y A182419 Cf. A182310, A182417, A182418
%K A182419 nonn,base
%O A182419 0,3
%A A182419 _Alex Ratushnyak_, Apr 27 2012