A135018 Triangle read by rows: row 1 = {1}, row 2 = {1,2}. Row n consists of the smallest n distinct positive integers such that no term in row (n-1) is the average of a term in row (n-2) and a term in row n.

1, 1, 2, 2, 4, 5, 1, 4, 5, 10, 1, 2, 7, 9, 10, 2, 5, 6, 7, 11, 12, 6, 16, 18, 19, 24, 25, 26, 2, 3, 4, 8, 9, 11, 12, 13, 9, 11, 13, 14, 15, 17, 19, 21, 22, 1, 2, 3, 4, 8, 12, 37, 43, 44, 45, 4, 6, 8, 12, 14, 16, 17, 18, 19, 20, 21, 2, 17, 18, 19, 42, 43, 44, 45, 46, 47, 48, 49

Offset

1,3

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Rémy Sigrist, PARI program

Example

Triangle begins:
1;
1,2;
2,4,5;
1,4,5,10;
1,2,7,9,10;
2,5,6,7,11,12;
etc.
Look at row 3 (2,4,5) and row 5 (1,2,7,9,10). The averages of the terms in row 3 with the terms of row 5 are: (2+1)/2 = 1.5, (2+2)/2=2, (2+7)/2=4.5; and continuing, the averages are: 5.5, 6, (4+1)/2= 2.5, 3, 5.5, 6.5, 7, (5+1)/2=3, 3.5, 6, 7, 7.5. None of these averages occur among the terms of row 4 (1,4,5,10). In fact, the terms of row 5 are the smallest 5 distinct positive integers such that the averages with the terms of row 3 do not equal any of the terms of row 4.

Prog

(PARI) See Links section.

Crossrefs

Sequence in context: A059372 A161422 A049261 * A073018 A201509 A109295

Adjacent sequences: A135015 A135016 A135017 * A135019 A135020 A135021

Keyword

nonn,tabl

Author

Leroy Quet, Feb 28 2008

Extensions

More terms from Rémy Sigrist, Jun 12 2022

Status

approved