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

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

Author

Alex Ratushnyak, Apr 27 2012

Keywords

• nonn
• base
• look

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

• Ivan Neretin, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A182310, A182417.

Programs

C

#include 
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

Mathematica

NestList[BitXor[#, Quotient[#, 6]] + 1 &, 0, 63] (* Ivan Neretin, Sep 03 2015 *)

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 */