

A265386


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


3



1, 1, 3, 2, 7, 4, 15, 9, 31, 19, 63, 39, 126, 79, 253, 158, 510, 315, 1012, 622, 2004, 1116, 4072, 2505, 8173, 5100, 16175, 10171, 32657, 20192, 64797, 39858, 128257, 71450, 260628, 160367, 523085, 326498, 1035105, 651126, 2090065, 1292517, 4146840
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OFFSET

1,3


COMMENTS

This recurrence is reminiscent of Fibonacci's, except that in each step the arguments as well as the result are 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 to sqrt(2), with the consecutiveterms ratio s(n) = a(n)/a(n1) exhibiting large and persistent fluctuations around the mean value.


LINKS

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


EXAMPLE

r(10) = 1.417436..., r(1000) = 1.414393...
s(100) = 0.629..., s(101) = 3.210..., s(102) = 0.618...
s(10000) = 0.631..., s(10001) = 3.183..., s(10002) = 0.608...


PROG

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


CROSSREFS

Cf. A000045, A003188, A265385, A265387.
Sequence in context: A056434 A143292 A293447 * A075627 A281825 A011384
Adjacent sequences: A265383 A265384 A265385 * A265387 A265388 A265389


KEYWORD

nonn


AUTHOR

Stanislav Sykora, Dec 07 2015


STATUS

approved



