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A309945 a(n) = floor(n - sqrt(2*n-1)). 1

%I

%S 0,0,0,1,2,2,3,4,4,5,6,7,8,8,9,10,11,12,12,13,14,15,16,17,18,18,19,20,

%T 21,22,23,24,24,25,26,27,28,29,30,31,32,32,33,34,35,36,37,38,39,40,40,

%U 41,42,43,44,45,46,47,48,49,50,50,51,52,53,54,55,56,57,58,59,60,60

%N a(n) = floor(n - sqrt(2*n-1)).

%C The subsequence consisting of numbers that appear twice is A007590.

%C Sequence as triangle:

%C 0;

%C 0;

%C 0; 1, 2;

%C 2, 3, 4;

%C 4, 5, 6, 7, 8;

%C 8, 9, 10, 11, 12;

%C 12, 13, 14, 15, 16, 17, 18;

%C 18, 19, 20, 21, 22, 23, 24;

%C ...

%C a(1) = 0; for n > 1, a(n) is the number of squares strictly between 2*n - 2 and n^2.

%H <a href="/A309945/b309945.txt">Table of n, a(n) for n = 1..999</a>

%F a(n) = n-1-floor(sqrt(2*n-2)). - _Wesley Ivan Hurt_, Dec 03 2020

%e For n = 3, 2*n - 2 = 4, n^2 = 9, no square numbers strictly between 4 and 9, a(3) = 0.

%e For n=5, 2*n - 2 = 8, n^2 = 25, two square numbers (9, 16) strictly between 8 and 25, a(5) = 2.

%t Table[Floor[n-(2*n-1)^(1/2)],{n,73}] (* _Stefano Spezia_, Aug 24 2019 *)

%o (PARI) a(n) = floor(n - sqrt(2*n-1)); \\ _Jinyuan Wang_, Aug 26 2019

%Y Cf. A007590, A080476, A016813.

%K nonn

%O 1,5

%A _Zhandos Mambetaliyev_, Aug 24 2019

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Last modified July 29 12:51 EDT 2021. Contains 346346 sequences. (Running on oeis4.)