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 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. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A289126 A062097 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

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)