A124110 -id:A124110 - cp's OEIS frontend

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

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

nonn

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).

			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, ...

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

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}]

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.

Original entry on oeis.org

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

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

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).

			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, ...

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

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

cp's OEIS Frontend

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.

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