A125765 Consider the array T(n, m) = m-th prime of the form n*i(i+1)/2 +/- 1. This sequence is the main diagonal.

2, 5, 19, 13, 181, 59, 463, 439, 2699, 281, 2309, 541, 8191, 2141, 6091, 3697, 11321, 1889, 38303, 7019, 24697, 8933, 42089, 11159, 39901, 21319, 61507, 21839, 266221, 17851, 182467, 37633, 104281, 102103, 173249, 40609, 386279, 32719, 229553

Offset

1,1

Comments

T(n, m) is a prime 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).

Links

Table of n, a(n) for n=1..39.

Example

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, ...

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, n], {n, 40}]

Crossrefs

Cf. A000217, A124110, A125766, A125767, A125768, A125769.

Sequence in context: A062097 A356366 A323706 * A068873 A035091 A045367

Adjacent sequences: A125762 A125763 A125764 * A125766 A125767 A125768

Keyword

nonn

Author

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

Status

approved