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A087059 Difference between 2 * n^2 and the next greater square number. 9
2, 1, 7, 4, 14, 9, 2, 16, 7, 25, 14, 1, 23, 8, 34, 17, 47, 28, 7, 41, 18, 56, 31, 4, 46, 17, 63, 32, 82, 49, 14, 68, 31, 89, 50, 9, 71, 28, 94, 49, 2, 72, 23, 97, 46, 124, 71, 16, 98, 41, 127, 68, 7, 97, 34, 128, 63, 161, 94, 25, 127, 56, 162, 89, 14, 124, 47, 161, 82, 1, 119 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n >= 2, a(n) is also the smallest absolute value of all negative values in row n of the triangle D(n, m) = n^2 - m^2 - 2*n*m, for 2 <= m+1 <= n. The negative values in row n start with m = floor(n/(1+sqrt(2))) + 1 = ceiling(n/(1+sqrt(2)) ). See also a comment on A087056 for the smallest positive numbers in row n >= 3. - Wolfdieter Lang, Jun 11 2015

LINKS

Table of n, a(n) for n=1..71.

FORMULA

a(n) = A087058(n) - 2*n^2 = A087057(n)^2 - 2*n^2 = (1 + A001951(n))^2 - 2*n^2 = (1 + floor[n*sqrt(2)])^2 - 2*n^2.

a(n) = 2*c(n)^2 - (n - c(n))^2, with c(n) := ceiling(n/(1 + sqrt(2))), n >= 1. - Wolfdieter Lang, Jun 11 2015

EXAMPLE

a(10) = 25 because the difference between 2*10^2 = 200 and the next greater square number (225) is 25.

PROG

(PARI) a(n) = (1 + sqrtint(2*n^2))^2 - 2*n^2 \\ Michel Marcus, Jun 25 2013

CROSSREFS

Cf. A001951, A087055, A087056, A087057, A087058, A087060.

Sequence in context: A075085 A217458 A124048 * A120872 A204771 A141512

Adjacent sequences:  A087056 A087057 A087058 * A087060 A087061 A087062

KEYWORD

easy,nonn

AUTHOR

Jens Voß, Aug 07 2003

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)