A337656 a(1)=0; thereafter, a(n) is the smallest number such that the addition table for (a(1),...,a(n)) contains n*(n+1)/2 different entries, and the multiplication table for (a(2),...,a(n)) contains n*(n-1)/2 different nonzero entries (the maximum possible in both cases).

0, 1, 3, 7, 12, 20, 30, 44, 65, 91, 107, 122, 147, 196, 230, 263, 329, 375, 397, 472, 545, 596, 677, 716, 770, 931, 1007, 1059, 1201, 1330, 1415, 1484, 1570, 1688, 1934, 1982, 2229, 2391, 2550, 2646, 2837, 3078, 3138, 3208, 3383, 3560, 3596, 3930, 4257, 4421, 4673

Offset: 1

Author

N. J. A. Sloane, Oct 01 2020

Keywords

• nonn

Comments

Inspired by A337655.

The distinct entries in the addition table for a(1),...,a(n), when sorted into increasing order, converge to a sequence which consists of all positive numbers except 5, 9, 11, 16, 17, 18, 22, 25, 26, 28, ... (see A337657).

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..3000 (first 87 terms from N. J. A. Sloane)
• Rémy Sigrist, C++ program for A337656

Crossrefs

Cf. A337655, A337657, A337658.

Extensions

Corrected and extended by Jean-Paul Delahaye, Oct 01 2020