A297615 Triangular array T(n, k) read by rows, n > 0, 0 < k <= n: T(n, k) = least unused positive value (reading rows from left to right) such that each triple of pairwise adjacent terms sums to a prime.

1, 2, 4, 6, 5, 8, 3, 20, 16, 7, 10, 18, 23, 14, 22, 12, 9, 26, 24, 35, 32, 11, 38, 36, 17, 30, 42, 15, 28, 34, 29, 44, 66, 31, 40, 46, 48, 21, 76, 58, 47, 54, 78, 45, 60, 13, 70, 82, 33, 88, 56, 41, 74, 62, 27, 50, 68, 59, 52, 72, 19, 136, 64, 43, 92, 80, 84

Offset: 1

Author

Rémy Sigrist, Jan 01 2018

Keywords

• nonn
• tabl

Comments

Each term may be involved in up to six sums:

- T(1, 1) is involved in one sum,

- For any r > 1, T(r, 1) and T(r, r) are involved in three sums:

- For any r > 1 and c such that 1 < c < r, T(r, c) is involved in six sums.

Among each triple of pairwise adjacent terms, we cannot have all values equal mod 3 or all values distinct mod 3; this gives rise to the patterns visible in the illustration in the Links section.

T(n, k) is odd iff n + k == 2 mod 3.

See also A297673 for a similar triangle.

Examples

			Triangle begins:
   1:                       1
   2:                     2,  4
   3:                   6,  5,  8
   4:                 3, 20, 16,  7
   5:              10, 18, 23, 14, 22
   6:            12,  9, 26, 24, 35, 32
   7:          11, 38, 36, 17, 30, 42, 15
   8:        28, 34, 29, 44, 66, 31, 40, 46
   9:      48, 21, 76, 58, 47, 54, 78, 45, 60
  10:    13, 70, 82, 33, 88, 56, 41, 74, 62, 27
The term T(1, 1) = 1 is involved in the following sum:
  -  1 +  2 +  4 =   7.
The term T(4, 4) = 7 is involved in the following sums:
  -  8 + 16 +  7 =  31,
  - 16 +  7 + 14 =  37,
  -  7 + 14 + 22 =  43.
The term T(7, 6) = 42 is involved in the following sums:
  - 35 + 32 + 42 = 109,
  - 35 + 30 + 42 = 107,
  - 32 + 42 + 15 =  89,
  - 30 + 42 + 31 = 103,
  - 42 + 31 + 40 = 113,
  - 42 + 15 + 40 =  97.
		

Links

• Rémy Sigrist, Rows n = 1..100, flattened
• Rémy Sigrist, PARI program for A297615
• Rémy Sigrist, Colored representation of the first 500 rows (where the color is function of T(n, k) mod 3)

Crossrefs

Cf. A297673.

Programs

PARI

See Links section.