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

1,3

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

Prog

(C++) See Links section.

Crossrefs

Cf. A337655, A337657, A337658.

Sequence in context: A002049 A025582 A247556 * A029452 A367892 A365043

Adjacent sequences: A337653 A337654 A337655 * A337657 A337658 A337659

Keyword

nonn

Author

N. J. A. Sloane, Oct 01 2020

Extensions

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

Status

approved