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A340507 a(n) = floor(sqrt(2*n)) - A003056(n). 1

%I #14 Aug 09 2022 11:00:59

%S 0,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,

%T 1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,

%U 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

%N a(n) = floor(sqrt(2*n)) - A003056(n).

%C This is A172471 - A003056.

%C Conjecture: This is an unsigned version of A072785.

%H Alois P. Heinz, <a href="/A340507/b340507.txt">Table of n, a(n) for n = 0..20000</a>

%o (PARI) a(n) = sqrtint(2*n) - (sqrtint(8*n+1)-1)\2; \\ _Michel Marcus_, Jan 25 2021

%o (Python)

%o from math import isqrt

%o def A340507(n): return isqrt(m:=n<<1)-(isqrt((m<<2)+1)-1>>1) # _Chai Wah Wu_, Aug 09 2022

%Y Cf. A003056, A072785, A172471.

%K nonn

%O 0

%A _N. J. A. Sloane_, Jan 25 2021

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