A165794 Nimsum of pairs of consecutive Lucas numbers.

3, 2, 7, 3, 12, 25, 15, 50, 99, 55, 188, 389, 843, 322, 1567, 3531, 1388, 7009, 12823, 8082, 25739, 50479, 24828, 94029, 203347, 436994, 169975, 812115, 1793132, 911369, 3247295, 6798738, 3281747, 12244295, 33047100, 13090261, 46475931, 101575874, 223888367, 97415931, 464656140

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Formula

a(n) = A003987(Lucas(n), Lucas(n+1)). - Michel Marcus, Apr 30 2019

Example

For n = 3, Lucas numbers are 4 and then 7. 0100 XOR 0111 = 0011 (3 in decimal).

Maple

read("transforms") ; A000032 := proc(n) option remember; if n <= 1 then op(n+1, [2, 1]) ; else procname(n-1)+procname(n-2) ; fi; end: A165794 := proc(n) nimsum(A000032(n), A000032(n+1)) ; end: seq(A165794(n), n=0..80) ; # R. J. Mathar, Sep 28 2009

Mathematica

BitXor @@@ Partition[LucasL[Range[0, 50]], 2, 1] (* Paolo Xausa, Apr 20 2026 *)

Prog

(Python)
a = 2
b = 1
while b < 2000:
    c = a^b
    print(c)
    a, b = b, a+b

Crossrefs

Nimsum of consecutive pairs in A000032.

Cf. A003987.

Sequence in context: A295422 A241838 A241559 * A075270 A067872 A318457

Adjacent sequences: A165791 A165792 A165793 * A165795 A165796 A165797

Keyword

nonn

Author

Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009

Extensions

More terms from R. J. Mathar, Sep 28 2009

More terms from Paolo Xausa, Apr 20 2026

Status

approved