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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.
2
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, 37, 36, 35, 39, 34, 40, 47, 41, 48, 57, 49, 58, 52, 61, 56, 50, 59, 51, 60, 55, 63, 54, 64, 75, 72, 69, 79, 67, 73, 70, 78, 68, 80, 94, 82, 96, 113, 100, 117
OFFSET
0,3
COMMENTS
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).
Floor(100*log_2(indices of 2^x)):
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
Conjecture:
As n -> infinity, a(n) -> infinity.
LINKS
MATHEMATICA
NestList[BitXor[#, Quotient[#, 6]] + 1 &, 0, 63] (* Ivan Neretin, Sep 03 2015 *)
PROG
(C)
#include <stdio.h>
int main(int argc, char **argv) {
unsigned long long a=0, prev;
while(1) {
prev = a, a = (a^(a/6)) + 1;
printf("%llu, ", prev);
}
return 0; // indices of 2^x: see C program of A182310.
} // from Alex Ratushnyak, Apr 27 2012
(PARI)
N=100; v=vector(N);
for (n=1, N-1, v[n+1] = bitxor( v[n], v[n] \ 6 ) + 1 );
v /* show terms */
/* Joerg Arndt, Apr 28 2012 */
CROSSREFS
Sequence in context: A059809 A327634 A121492 * A204580 A347831 A331206
KEYWORD
nonn,base,look
AUTHOR
Alex Ratushnyak, Apr 27 2012
STATUS
approved