A232234 Additive bases: a(n) is the least integer such that there is an n-element set of nonnegative integers, the sums of pairs of which are distinct and at most a(n).

0, 2, 6, 12, 22, 34, 50, 68, 88, 110, 144, 170, 212, 254, 302, 354, 398, 432, 492, 566, 666, 712, 744, 850, 960, 984, 1106

Offset: 1

Author

N. J. A. Sloane, Nov 24 2013

Keywords

• nonn
• more

Comments

By definition, these terms are twice the terms of A003022, see comment there. - Bernd Mulansky, Jun 25 2021

Lexicographically first basis that yields a(16) = 354 is {0,1,4,11,26,32,56,68,76,115,117,134,150,163,168,177}. - Fausto A. C. Cariboni, Nov 01 2017

Lexicographically first basis that yields a(17) = 398 is {0,5,7,17,52,56,67,80,81,100,122,138,159,165,168,191,199}. - Fausto A. C. Cariboni, Nov 26 2017

Links

• Fausto A. C. Cariboni, All additive bases that yield a(n) for n = 2..17, Dec 31 2017.
• Z. Skupien and A. Zak, Pair-sums packing and rainbow cliques, in Topics In Graph Theory, A tribute to A. A. and T. E. Zykovs on the occasion of A. A. Zykov's 90th birthday, ed. R. Tyshkevich, Univ. Illinois, 2013, pages 131-144 (in English and Russian).

Crossrefs

These terms are twice the terms of A003022.

See A004133 for another version.

Extensions

a(16) from Fausto A. C. Cariboni, Nov 01 2017

a(17) from Fausto A. C. Cariboni, Nov 26 2017

a(18)-a(27) added by Bernd Mulansky, Jun 25 2021