A337946 - OEIS

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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).

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