A035305 Minimum sum of n distinct positive numbers, any n-1 of which sum to a square.

1, 5, 55, 122, 633, 911, 2210, 3156, 4908, 8656, 13018, 17426, 25968, 33135, 45374, 57128, 74543, 93673, 116973, 144454, 175564, 207031, 258150, 304708, 362466, 416117, 490029, 562590, 660993, 756963, 855786, 984152, 1106930, 1243237, 1413817, 1587606, 1766365, 1965706, 2181532, 2393220

Offset

1,2

Links

Max Alekseyev, Table of n, a(n) for n = 1..300

Haikin Fedor, Table for partition problem (1998)

Formula

a(n) = smallest integer s such that there exist nonnegative integers x1 < x2 < ... < xn < sqrt(s) satisfying s*(n-1) = x1^2 + x2^2 + ... + xn^2. The n numbers stated in the definition are then given by s-x1^2, ..., s-xn^2. - Max Alekseyev, May 29 2024

Example

a(2)=5 because 5=1+4 and both 1 and 4 are squares.
a(3)=55 because 55=6+19+30 and all three of 25=6+19, 36=6+30 and 49=19+30 are squares.

Crossrefs

Sequence in context: A216446 A307991 A015221 * A292455 A292735 A057722

Adjacent sequences: A035302 A035303 A035304 * A035306 A035307 A035308

Keyword

nonn,nice

Author

Erich Friedman, Steven Finch

Extensions

Link edited by N. J. A. Sloane, Jan 26 2009 at the suggestion of Steven Finch.

a(1)=1 prepended by Max Alekseyev, May 21 2022

Terms a(31) onward from Max Alekseyev, May 29 2024

Status

approved