

A265385


Sequence defined by a(1)=a(2)=1 and a(n) = gray(a(n1) + a(n2)), with gray(m) = A003188(m).


3



1, 1, 3, 6, 13, 26, 52, 105, 211, 418, 847, 1673, 3380, 6755, 13404, 27104, 53538, 108163, 216183, 428935, 867329, 1713228, 3461227, 6917868, 13725948, 27754524, 54823316, 110759272, 221371778, 439230367, 888144817, 1754346232, 3544296957, 7083888783
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

This recurrence is reminiscent of Fibonacci's, except that the result of each step is passed through the binaryreflected Gray code mapping, which introduces a degree of pseudorandomness.
Conjecture: The mean growth rate r(n) = (a(2n)/a(n))^(1/n) appears to converge exactly to 2, with the consecutiveterms ratio s(n) = a(n)/a(n1) exhibiting relatively small (~1%) but persistent fluctuations around the mean value. This contrasts what one might first expect, that sequence's growth rate were similar to that of the Fibonacci sequence, i.e., the golden ratio, since gray(m) just permutes every block of numbers ranging from 2^k to 2^l1, for any 0<k<l.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..1000
Wikipedia, Fibonacci number
Wikipedia, Gray code


EXAMPLE

r(10) = 2.000421531046..., r(1000) = 1.999999999903...
s(100) = 1.9841292..., s(101) = 2.0220518..., s(102) = 1.9752921...
s(10000) = 1.9841299..., s(10001) = 2.0220478..., s(10002) = 1.9752929...


PROG

(PARI) gray(m)=bitxor(m, m>>1);
a=vector(1000); a[1]=1; a[2]=1; for(n=3, #a, a[n]=gray(a[n1]+a[n2])); a


CROSSREFS

Cf. A000045, A003188, A265386, A265387.
Sequence in context: A079941 A255125 A267367 * A019300 A072762 A081254
Adjacent sequences: A265382 A265383 A265384 * A265386 A265387 A265388


KEYWORD

nonn


AUTHOR

Stanislav Sykora, Dec 07 2015


STATUS

approved



