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A080343
a(n) = round(sqrt(2*n)) - floor(sqrt(2*n)).
3
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
0,1
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
PROG
(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
CROSSREFS
Sequence in context: A341999 A118685 A244063 * A011664 A179831 A094091
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 20 2003
STATUS
approved