A302706 a(n) is the maximum remainder of x^2 + y^2 divided by x + y with 0 < x <= y <= n.

0, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 16, 18, 18, 18, 26, 27, 28, 29, 30, 32, 32, 33, 34, 35, 40, 40, 40, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 72, 72, 72, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 98, 98, 98, 98, 98, 98, 99, 100, 104, 104, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132

Offset

1,2

Comments

Values of a(n) such that a(n) is prime are 2, 3, 5, 11, 13, 29, 53, 59, 61, 83, 89, 127, 131, 137, 139, 173, ...

Conjecture: lim_{n->inf} a(n)/(2n) = 1, with both variables x and y taking values asymptotically close to n. - Andres Cicuttin, Oct 18 2018

Links

Altug Alkan, Table of n, a(n) for n = 1..1000

Example

a(1) = 0 because x = y = 1 is only option.
a(13) = a(14) = a(15) = 18 because (7^2 + 13^2) mod (7 + 13) = 18 is the largest corresponding remainder for them.

Mathematica

a[n_]:=Table[Table[Mod[x^2+y^2 , x+y], {x, 1, y}], {y, 1, n}]//Flatten//Max;
Table[a[n], {n, 1, 100}]

Prog

(PARI) a(n) = vecmax(vector(n, x, vecmax(vector(x, y, (x^2+y^2) % (x+y))))); \\ after Michel Marcus at A302245

Crossrefs

Cf. A053626, A302245.

Sequence in context: A037476 A007093 A285469 * A047423 A032970 A137691

Adjacent sequences: A302703 A302704 A302705 * A302707 A302708 A302709

Keyword

nonn,easy

Author

Altug Alkan and Andres Cicuttin, Apr 12 2018

Status

approved