A195898 Smallest possible largest number in a set of n integers such that the sum of any two numbers is a positive cube.

1, 14, 70993724

Offset

2,2

Comments

Here, the smallest number is negative (since we need the smallest such largest number) and the remaining numbers are positive (since the condition is about positive cubes).

Links

Table of n, a(n) for n=2..4.

Erich Friedman, Problem of the month October 2010

Andrzej Nowicki, Podroze po Imperium Liczb [broken link]

Example

{ -35780, 4693243, 11888132, 70993724 } is the smallest set of 4 numbers such that all 6 combinations of sum of any two numbers is a perfect cube. For example, -35780 + 70993724 = 414^3 and 4693243 + 11888132 = 255^3.
{ -13, 13, 14 } is the smallest set of 3 numbers where all 3 combinations of sum of any two numbers is a perfect cube.
{ -1, 1 } is the trivial set of two numbers because -1 + 1 = 0^3.

Crossrefs

Cf. A000578, A195854, A195899.

Sequence in context: A350891 A347626 A013870 * A263500 A164526 A278897

Adjacent sequences: A195895 A195896 A195897 * A195899 A195900 A195901

Keyword

nonn,more,bref

Author

Kausthub Gudipati, Sep 25 2011

Status

approved