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A337946 a(1)=1; thereafter, a(n) is the smallest number such that the addition and multiplication tables for (a(1),...,a(n)) together contain n*(n+1) different entries (the maximum possible). 9
1, 3, 7, 12, 22, 30, 47, 61, 85, 113, 126, 177, 193, 246, 279, 321, 341, 428, 499, 571, 616, 686, 754, 854, 975, 1052, 1150, 1317, 1376, 1457, 1513, 1664, 1761, 1961, 2307, 2434, 2591, 2795, 2843, 3057, 3226, 3405, 3508, 3776, 3930, 4023, 4196, 4575, 4731 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Peter Kagey, Table of n, a(n) for n = 1..1000

Peter Kagey, Haskell program

EXAMPLE

The addition table of a(k) for k=1..5:

   + | 1 3  7 12 22

  ---+-------------

   1 | 2 4  8 13 23

   3 |   6 10 15 25

   7 |     14 19 29

  12 |        24 34

  22 |           44

The multiplication table of a(k) for k=1..5:

   * | 1 3  7  12  22

  ---+---------------

   1 | 1 3  7  12  22

   3 |   9 21  36  66

   7 |     49  84 154

  12 |        144 264

  22 |            484

These two tables contain the 5*(5+1) = 30 values {1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 19, 21, 22, 23, 24, 25, 29, 34, 36, 44, 49, 66, 84, 144, 154, 264, 484}.

MATHEMATICA

j={k=1}; Do[While[l=Join[j, {++k}]; g=Union[Sort/@Tuples[l, {2}]]; p=Times@@#&/@g; s=Total/@g; !SameQ@@Flatten[{Length@Union@Flatten@{p, s}, Length@l(Length@l+1)}]]; j=Join[j, {k}]; k=Last@j, 48]; j (* Giorgos Kalogeropoulos, Nov 16 2021 *)

CROSSREFS

Cf. A005282 (addition table), A066720 (multiplication table), A337655, A337656, A337947.

Sequence in context: A034434 A243190 A256483 * A345433 A344856 A262567

Adjacent sequences:  A337943 A337944 A337945 * A337947 A337948 A337949

KEYWORD

nonn

AUTHOR

Peter Kagey, Oct 02 2020

STATUS

approved

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)