Pairs of numbers (j,k) that produce the primes in S000615.

2, 3, 1, 4, 5, 8, 7, 10, 6, 11, 12, 13, 9, 16, 14, 15, 17, 18, 20, 23, 19, 24, 21, 26, 22, 27, 25, 28, 30, 31, 29, 34, 32, 33, 35, 36, 37, 40, 39, 44, 38, 45, 42, 43, 47, 48, 46, 49, 50, 53, 51, 56, 52, 57, 41, 66, 54, 59, 55, 62, 58, 63, 60, 67, 65, 68, 61, 76

1

Every number appears only once. The n-th pair produces the n-th prime in S000615

T. D. Noe, Plot of 500 pairs

T. D. Noe, Table of 500 pairs

(Mma) n = 100; lst = Reverse[Range[2 n]]; prms = {}; Do[m = lst[[1]]; lst = Delete[lst, 1]; pos = 1; While[p = m^2 + lst[[pos]]^2; Not[PrimeQ[p]], pos++]; AppendTo[prms, {p, lst[[pos]], m}]; lst = Delete[lst, pos], {i, n}]; t2 = Take[Sort[prms], n/2]; Flatten[Transpose[Take[Transpose[t2], -2]]]

Cf. S000615.

nonn,tabl

T. D. Noe, May 05 2015