A125766 Consider the array T(n, m) = m-th prime of the form n*i(i+1)/2 +- 1. This sequence is read by antidiagonals.

2, 3, 5, 2, 5, 7, 3, 17, 7, 11, 29, 5, 19, 11, 29, 5, 31, 11, 29, 13, 37, 41, 7, 139, 13, 31, 19, 67, 7, 43, 17, 179, 23, 83, 29, 79, 53, 23, 71, 19, 181, 41, 107, 31, 137, 11, 89, 47, 197, 37, 331, 59, 109, 41, 191, 67, 29, 251, 79, 251, 59, 389, 61, 197, 43, 211, 11, 109, 31

Offset: 1

Author

Jonathan Vos Post & Robert G. Wilson v, Dec 01 2006

Keywords

• nonn
• tabl

Comments

T(n, m) is the m-th prime in order which is n times some triangular number plus or minus 1.

Eventually all primes, p, appear since (p +-1) times 1(1+1)/2 equals (p +- 1).

Examples

			1 | 2, 5, 7, 11, 29, 37, 67, 79, 137, 191, 211, 277, 379, 631, 821, ...
2 | 3, 5, 7, 11, 13, 19, 29, 31, 41, 43, 71, 73, 89, 109, 131, ...
3 | 2, 17, 19, 29, 31, 83, 107, 109, 197, 199, 233, 359, 409, 569, 571, ...
4 | 3, 5, 11, 13, 23, 41, 59, 61, 83, 113, 179, 181, 263, 311, 313, ...
5 | 29, 31, 139, 179, 181, 331, 389, 599, 601, 1049, 1051, 1381, 1499, 1889, 2029, ...
6 | 5, 7, 17, 19, 37, 59, 61, 89, 127, 167, 269, 271, 331, 397, 467, ...
7 | 41, 43, 71, 197, 251, 461, 463, 547, 839, 953, 1471, 1931, 1933, 2099, 2647, ...
8 | 7, 23, 47, 79, 167, 223, 359, 439, 727, 839, 1087, 1223, 1367, 1847, 2207, ...
9 | 53, 89, 251, 593, 701, 1223, 1709, 1889, 2699, 4463, 4751, 5669, 7019, 8513,10151, ...
10 | 11, 29, 31, 59, 61, 101, 149, 151, 211, 281, 359, 449, 659, 661, 911, ...
11 | 67, 109, 307, 397, 727, 857, 859, 1319, 1321, 2089, 2309, 2311, 3037, 3299, 3301, ...
		

Crossrefs

Cf. A000217, A124110, A125765, A125767, A125768, A125769.

Programs

Mathematica

T[n_, m_] := Block[{c = 0, k = 1, s = {}, trnglr}, While[c < m + 1, trnglr = n*k(k + 1)/2; If[ PrimeQ[trnglr - 1], c++; AppendTo[s, trnglr - 1]]; If[PrimeQ[trnglr + 1], c++; AppendTo[s, trnglr + 1]]; k++; s = Union@s]; s[[m]] ]; Table[ T[n - m + 1, m], {n, 12}, {m, n}] // Flatten