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%I #11 Aug 19 2016 04:33:38
%S 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,
%T 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,
%U 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
%N a(n) = round(sqrt(2*n)) - floor(sqrt(2*n)).
%H Chai Wah Wu, <a href="/A080343/b080343.txt">Table of n, a(n) for n = 0..10000</a>
%F 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, ...
%F 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.
%F a(n) = A023969(2*n). - _Michel Marcus_, Aug 19 2016
%o (Python)
%o from gmpy2 import isqrt_rem
%o def A080343(n):
%o i, j = isqrt_rem(2*n)
%o return int(4*(j-i) >= 1) # _Chai Wah Wu_, Aug 16 2016
%Y Cf. A023969, A080352.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Mar 20 2003
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