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%I #47 Nov 16 2021 05:50:17
%S 1,2,5,7,15,22,31,50,68,90,101,124,163,188,215,253,322,358,455,486,
%T 527,631,702,780,838,920,1030,1062,1197,1289,1420,1500,1689,1765,1886,
%U 2114,2353,2410,2570,2686,2857,3063,3207,3477,3616,3845,3951,4150,4480,4595,4746,5030,5286,5698,5999,6497,6624,6938,7219,7661,7838,8469,8665,9198,9351,9667,9966
%N a(1)=1; thereafter, a(n) is the smallest number such that both the addition and multiplication tables for (a(1),...,a(n)) contain n*(n+1)/2 different entries (the maximum possible).
%C If one specifies that not only are there n(n+1)/2 distinct numbers in the addition and multiplication tables, but that all n(n+1) numbers are distinct, then the sequence is A337946 - _David A. Corneth_, Oct 02 2020
%H Rémy Sigrist, <a href="/A337655/b337655.txt">Table of n, a(n) for n = 1..3000</a> (a(1)-a(101) from Jean-Paul Delahaye, a(102)-a(1000) from Peter Kagey)
%H Rémy Sigrist, <a href="/A337655/a337655.txt">C++ program for A337655</a>
%t terms=67;a[1]=b[1]=1;a1=b1={1};Do[k=a[n-1]+1;While[a2=Union@Join[{2k},Array[a@#+k&,n-1]];b2=Union@Join[{k^2},Array[b@#*k&,n-1]];Intersection[a2,a1]!={}||Intersection[b2,b1]!={},k++];a[n]=b[n]=k;a1=Union[a1,a2];b1=Union[b1,b2],{n,2,terms}];Array[a,terms] (* _Giorgos Kalogeropoulos_, Nov 15 2021 *)
%o (C++) See Links section.
%Y See A337659 and A337660 (for the addition table), and A337661 and A337662 (for the multiplication table).
%Y Cf. A337656, A337657, A337658.
%Y For similar sequences that focus just on the addition or multiplication tables, see A005282 and A066720.
%Y Cf. also A337946.
%K nonn
%O 1,2
%A _Jean-Paul Delahaye_, Sep 30 2020
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