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

1,1

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).

Links

Table of n, a(n) for n=1..69.

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 - m + 1, m], {n, 12}, {m, n}] // Flatten

Crossrefs

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

Sequence in context: A167835 A102044 A370590 * A093870 A250445 A297996

Adjacent sequences: A125763 A125764 A125765 * A125767 A125768 A125769

Keyword

nonn,tabl

Author

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

Status

approved