cp's OEIS Frontend

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).

%I A337656 #34 Oct 02 2020 11:13:19
%S A337656 0,1,3,7,12,20,30,44,65,91,107,122,147,196,230,263,329,375,397,472,
%T A337656 545,596,677,716,770,931,1007,1059,1201,1330,1415,1484,1570,1688,1934,
%U A337656 1982,2229,2391,2550,2646,2837,3078,3138,3208,3383,3560,3596,3930,4257,4421,4673
%N 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).
%C A337656 Inspired by A337655.
%C A337656 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).
%H A337656 Rémy Sigrist, <a href="/A337656/b337656.txt">Table of n, a(n) for n = 1..3000</a> (first 87 terms from N. J. A. Sloane)
%H A337656 Rémy Sigrist, <a href="/A337656/a337656.txt">C++ program for A337656</a>
%o A337656 (C++) See Links section.
%Y A337656 Cf. A337655, A337657, A337658.
%K A337656 nonn
%O A337656 1,3
%A A337656 _N. J. A. Sloane_, Oct 01 2020
%E A337656 Corrected and extended by _Jean-Paul Delahaye_, Oct 01 2020