A182508 a(0)=0, a(1)=1, a(n) = (a(n-2)+a(n-1)+n) AND n.

0, 1, 2, 2, 0, 5, 2, 6, 0, 9, 2, 2, 0, 13, 10, 6, 0, 17, 2, 2, 16, 5, 2, 22, 16, 25, 2, 18, 16, 29, 10, 6, 32, 1, 2, 34, 0, 5, 34, 6, 0, 41, 2, 2, 32, 13, 10, 6, 0, 49, 34, 2, 16, 5, 2, 54, 48, 25, 2, 18, 16, 29, 42, 6, 64, 1, 2, 66, 0, 5, 66, 6

Offset

0,3

Comments

Terms with indices 4*k+1 are odd, all other terms are even.

Conjecture: sequence contains infinitely many zeros and ones, but no terms of the form 2^k-1, k>1.

Links

Table of n, a(n) for n=0..71.

Formula

a(0)=0, a(1)=1, a(n) = (a(n-2)+a(n-1)+n) AND n, where AND is the bitwise AND operator.

Mathematica

nxt[{n_, a_, b_}]:={n+1, b, BitAnd[a+b+n+1, n+1]}; NestList[nxt, {1, 0, 1}, 80][[All, 2]] (* Harvey P. Dale, Nov 19 2021 *)

Prog

(Python)
prpr = 0
prev = 1
for n in range(2, 99):
  current = (prpr + prev + n) & n
  print prpr,
  prpr = prev
  prev = current

Crossrefs

Sequence in context: A291483 A181295 A166299 * A213626 A329687 A356035

Adjacent sequences: A182505 A182506 A182507 * A182509 A182510 A182511

Keyword

nonn,base,easy

Author

Alex Ratushnyak, May 03 2012

Status

approved