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A182418 a(0)=0, a(n+1) = (a(n) XOR floor(a(n)/6)) + 1, where XOR is the bitwise exclusive-or operator.

%I A182418 #18 Aug 17 2025 21:12:12
%S A182418 0,1,2,3,4,5,6,8,10,12,15,14,13,16,19,17,20,24,29,26,31,27,32,38,33,
%T A182418 37,36,35,39,34,40,47,41,48,57,49,58,52,61,56,50,59,51,60,55,63,54,64,
%U A182418 75,72,69,79,67,73,70,78,68,80,94,82,96,113,100,117
%N A182418 a(0)=0, a(n+1) = (a(n) XOR floor(a(n)/6)) + 1, where XOR is the bitwise exclusive-or operator.
%C A182418 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 A182418 Floor(100*log_2(indices of 2^x)):
%C A182418 0, 100, 200, 280, 370, 445, 555, 614, 704, 761, 896, 1000, 1088, 1210, 1284, 1389, 1505, 1591, 1677, 1765, 1839, 1968, 2060, 2170, 2250, 2366, 2478, 2606, 2713, 2806, 2857, 2997, 3096, 3193, 3254, 3393, 3487, 3583, 3664, 3741, 3858, 3925, 4073, 4192, 4313, 4394, 4520
%C A182418 Conjecture:
%C A182418 As n -> infinity, a(n) -> infinity.
%H A182418 Ivan Neretin, <a href="/A182418/b182418.txt">Table of n, a(n) for n = 0..10000</a>
%t A182418 NestList[BitXor[#, Quotient[#, 6]] + 1 &, 0, 63] (* _Ivan Neretin_, Sep 03 2015 *)
%o A182418 (C)
%o A182418 #include <stdio.h>
%o A182418 int main(int argc, char **argv) {
%o A182418   unsigned long long a=0, prev;
%o A182418   while(1) {
%o A182418     prev = a,   a = (a^(a/6)) + 1;
%o A182418     printf("%llu, ", prev);
%o A182418   }
%o A182418   return 0;     // indices of 2^x: see C program of A182310.
%o A182418 }               // from _Alex Ratushnyak_, Apr 27 2012
%o A182418 (PARI)
%o A182418 N=100; v=vector(N);
%o A182418 for (n=1, N-1, v[n+1] = bitxor( v[n], v[n] \ 6 ) + 1 );
%o A182418 v /* show terms */
%o A182418 /* _Joerg Arndt_, Apr 28 2012 */
%Y A182418 Cf. A182310, A182417.
%K A182418 nonn,base,look
%O A182418 0,3
%A A182418 _Alex Ratushnyak_, Apr 27 2012