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A297615
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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.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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