OFFSET
1,5
COMMENTS
The subsequence consisting of numbers that appear twice is A007590.
Sequence as triangle:
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, 21, 22, 23, 24;
...
a(1) = 0; for n > 1, a(n) is the number of squares strictly between 2*n - 2 and n^2.
FORMULA
a(n) = n-1-floor(sqrt(2*n-2)). - Wesley Ivan Hurt, Dec 03 2020
EXAMPLE
For n = 3, 2*n - 2 = 4, n^2 = 9, no square numbers strictly between 4 and 9, a(3) = 0.
For n=5, 2*n - 2 = 8, n^2 = 25, two square numbers (9, 16) strictly between 8 and 25, a(5) = 2.
MATHEMATICA
Table[Floor[n-(2*n-1)^(1/2)], {n, 73}] (* Stefano Spezia, Aug 24 2019 *)
PROG
(PARI) a(n) = floor(n - sqrt(2*n-1)); \\ Jinyuan Wang, Aug 26 2019
(Python)
from math import isqrt
def A309945(n): return (m:=n-1)-isqrt(m<<1) # Chai Wah Wu, Aug 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhandos Mambetaliyev, Aug 24 2019
STATUS
approved