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A338012 a(1)=0; thereafter, a(n) is the smallest number such that the addition and multiplication tables for (a(1),...,a(n)) together contain n^2 different entries (the maximum possible).

%I A338012 #12 Oct 10 2020 03:56:45
%S A338012 0,3,4,10,18,23,34,55,67,93,95,120,149,166,228,271,351,398,439,505,
%T A338012 563,611,732,771,806,924,1052,1121,1278,1412,1586,1654,1875,2012,2245,
%U A338012 2341,2445,2616,2819,2920,3034,3322,3518,3754,3918,4016,4311,4649,4848,5321
%N A338012 a(1)=0; thereafter, a(n) is the smallest number such that the addition and multiplication tables for (a(1),...,a(n)) together contain n^2 different entries (the maximum possible).
%H A338012 Peter Kagey, <a href="/A338012/b338012.txt">Table of n, a(n) for n = 1..1000</a>
%e A338012 Addition table begins:
%e A338012    + |  0  3  4 10 18 23  34  55  67
%e A338012 -----+-------------------------------
%e A338012    0 |  0
%e A338012    3 |  3  6
%e A338012    4 |  4  7  8
%e A338012   10 | 10 13 14 20
%e A338012   18 | 18 21 22 28 36
%e A338012   23 | 23 26 27 33 41 46
%e A338012   34 | 34 37 38 44 52 57  68
%e A338012   55 | 55 58 59 65 73 78  89 110
%e A338012   67 | 67 70 71 77 85 90 101 122 134
%e A338012 Multiplication table begins:
%e A338012    * | 0   3   4  10   18   23   34   55   67
%e A338012 -----+---------------------------------------
%e A338012    0 | 0
%e A338012    3 | 0   9
%e A338012    4 | 0  12  16
%e A338012   10 | 0  30  40 100
%e A338012   18 | 0  54  72 180  324
%e A338012   23 | 0  69  92 230  414  529
%e A338012   34 | 0 102 136 340  612  782 1156
%e A338012   55 | 0 165 220 550  990 1265 1870 3025
%e A338012   67 | 0 201 268 670 1206 1541 2278 3685 4489
%Y A338012 Cf. A337655, A337656, A337946.
%Y A338012 Cf. A338013, A338014, A338015, A338016, A338017.
%K A338012 nonn
%O A338012 1,2
%A A338012 _Peter Kagey_, Oct 06 2020