A337655 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).

1, 2, 5, 7, 15, 22, 31, 50, 68, 90, 101, 124, 163, 188, 215, 253, 322, 358, 455, 486, 527, 631, 702, 780, 838, 920, 1030, 1062, 1197, 1289, 1420, 1500, 1689, 1765, 1886, 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

Offset

1,2

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..3000 (a(1)-a(101) from Jean-Paul Delahaye, a(102)-a(1000) from Peter Kagey)

Rémy Sigrist, C++ program for A337655

Mathematica

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 *)

Prog

(C++) See Links section.

Crossrefs

See A337659 and A337660 (for the addition table), and A337661 and A337662 (for the multiplication table).

Cf. A337656, A337657, A337658.

For similar sequences that focus just on the addition or multiplication tables, see A005282 and A066720.

Cf. also A337946.

Sequence in context: A215513 A358878 A306956 * A366175 A111328 A244962

Adjacent sequences: A337652 A337653 A337654 * A337656 A337657 A337658

Keyword

nonn

Author

Jean-Paul Delahaye, Sep 30 2020

Status

approved