A394409 Pascal-like triangle read by rows: top entry is 2; thereafter fill in entries from top to bottom, alternating between left to right and right to left, with the smallest number that is not yet in the sequence and has a common factor with any earlier entry that is adjacent to it in the triangle.

2, 4, 6, 3, 12, 8, 10, 14, 18, 9, 15, 21, 24, 16, 20, 5, 30, 22, 28, 35, 25, 40, 45, 42, 26, 32, 50, 55, 11, 44, 34, 36, 38, 48, 54, 46, 23, 69, 27, 57, 60, 51, 66, 33, 77, 7, 63, 39, 72, 68, 76, 78, 75, 115, 92, 52, 70, 65, 80, 56, 58, 62, 84, 81, 105, 49, 91

Offset

1,1

Comments

This is a variation of A397219 where the rows are filled from left to right and then right to left as the triangle is filled from the top. See that sequence for further details.

It is conjectured that every number greater than 1 appears.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..20000

Scott R. Shannon, Image of the first 1000 terms on the triangle. The number colors are graduated across the spectrum, from red to violet, to show their relative size.

Scott R. Shannon, Image of the first 100000 terms on the triangle.

Example

The triangle begins:
                       2,
                     4, 6,
                   8, 12, 3,
                 10, 14, 18, 9,
               20, 16, 24, 21, 15,
              5, 30, 22, 28, 35, 25,
           55, 50, 32, 26, 42, 45, 40,
          11, 44, 34, 36, 38, 48, 54, 46,
        77, 33, 66, 51, 60, 57, 27, 69, 23
.

Crossrefs

Cf. A397219, A064413, A007318, A397218.

Sequence in context: A329492 A163234 A366111 * A348022 A072984 A339671

Adjacent sequences: A394406 A394407 A394408 * A394410 A394411 A394413

Keyword

nonn

Author

Scott R. Shannon, Jun 20 2026

Status

approved