A165990 Nim sum of distinct consecutive pairs of Lucas Numbers.

3, 7, 12, 15, 99, 188, 843, 1567, 1388, 12823, 25739, 24828, 203347, 169975, 1793132, 3247295, 3281747, 33047100, 46475931, 223888367, 464656140, 443782407, 3392754203, 6320720892, 28126943139, 51929697511, 46812642508, 430604078639, 875439722435, 832171221180

Offset

0,1

Comments

The nim sum of two numbers is the bitwise exclusive-or of the numbers. - Andrew Howroyd, Apr 13 2021

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

a(n) = A000032(2*n) XOR A000032(2*n+1). - Andrew Howroyd, Apr 13 2021

Example

nim sum(2,1) = 3; nim sum(3,4)=7; nim sum(7,11) = 12; nim sum(18,29) = 15; nim sum(47,76) = 99; nim sum(123,199) = 188.

Prog

(PARI)
L(n)={fibonacci(n+1) + fibonacci(n-1)}
a(n)={bitxor(L(2*n), L(2*n+1))} \\ Andrew Howroyd, Apr 13 2021

Crossrefs

Cf. A000032.

Sequence in context: A122982 A101589 A061559 * A160998 A141205 A310237

Adjacent sequences: A165987 A165988 A165989 * A165991 A165992 A165993

Keyword

nonn

Author

Amal Dua (amaldua1992(AT)hotmail.com), Oct 03 2009

Extensions

Terms a(6) and beyond from Andrew Howroyd, Apr 13 2021

Status

approved