A080343 a(n) = round(sqrt(2*n)) - floor(sqrt(2*n)).

0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane, Mar 20 2003

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A023969, A080352.

Programs

Python

from gmpy2 import isqrt_rem
def A080343(n):
    i, j = isqrt_rem(2*n)
    return int(4*(j-i) >= 1) # Chai Wah Wu, Aug 16 2016

Formula

Runs are 0^1, 0^1, 0^2 1, 0^2 1, 0^3 1^2, 0^3 1^2, 0^4 1^3, 0^4 1^3, ...

a(n) = 1 iff n >= 4 and n is in the interval [t_k + 1, ..., t_k + floor(k/2)] for some k >= 2, where t_k = k*(k+1)/2 is a triangular number.

a(n) = A023969(2*n). - Michel Marcus, Aug 19 2016