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A309945
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a(n) = floor(n - sqrt(2*n-1)).
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1
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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, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 60
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listen;
history;
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internal format)
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OFFSET
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1,5
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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Table[Floor[n-(2*n-1)^(1/2)], {n, 73}] (* Stefano Spezia, Aug 24 2019 *)
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PROG
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(PARI) a(n) = floor(n - sqrt(2*n-1)); \\ Jinyuan Wang, Aug 26 2019
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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