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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).
10
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)
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).
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
KEYWORD
nonn
AUTHOR
Jean-Paul Delahaye, Sep 30 2020
STATUS
approved