A101650 A Thue-Morse-Stern sequence.

0, 0, 1, 0, 2, 1, 2, 0, 0, 2, 1, 1, 1, 2, 0, 0, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 0, 1, 0, 0, 2, 1, 1, 0, 1, 2, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 0, 0, 2, 1, 1, 1, 2, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 1, 1, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0

Offset

0,5

Links

Paolo Xausa, Table of n, a(n) for n = 0..16382

Formula

a(n) = mod(-1+Sum_{k=0..floor(n/2)} mod(binomial(n-k, k), 2), 3).

a(n) = mod(-1+A002487(n+1), 3).

a(2n+1) = a(n).

Mathematica

Mod[Flatten[NestList[Flatten[Transpose[{#, # + RotateLeft[#]}]] &, {1}, 6]] - 1, 3] (* Paolo Xausa, Aug 04 2025, after Takashi Tokita at A002487 *)

Prog

(Python)
from functools import reduce
def A101650(n): return (sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(n+1)[-1:2:-1], (1, 0)))-1)%3 # Chai Wah Wu, Jul 31 2025

Crossrefs

Cf. A002487, A010060.

Sequence in context: A348921 A050601 A383706 * A287411 A053796 A029391

Adjacent sequences: A101647 A101648 A101649 * A101651 A101652 A101653

Keyword

easy,nonn

Author

Paul Barry, Dec 10 2004

Status

approved