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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).
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%I #34 Oct 02 2020 11:13:19

%S 0,1,3,7,12,20,30,44,65,91,107,122,147,196,230,263,329,375,397,472,

%T 545,596,677,716,770,931,1007,1059,1201,1330,1415,1484,1570,1688,1934,

%U 1982,2229,2391,2550,2646,2837,3078,3138,3208,3383,3560,3596,3930,4257,4421,4673

%N 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 Inspired by A337655.

%C 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 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 Rémy Sigrist, <a href="/A337656/a337656.txt">C++ program for A337656</a>

%o (C++) See Links section.

%Y Cf. A337655, A337657, A337658.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Oct 01 2020

%E Corrected and extended by _Jean-Paul Delahaye_, Oct 01 2020