A362035 Numbers that occur three or more times in A362034.

2, 17, 29, 43, 59, 61, 83, 103, 107, 137, 167, 173, 211, 251, 257, 307, 359, 379, 419, 479, 499, 541, 613, 631, 673, 691, 761, 769, 853, 887, 937, 991, 1031, 1129, 1151, 1231, 1361, 1399, 1459, 1471, 1493, 1583, 1697, 1823, 1831, 1973, 2111, 2179, 2243, 2251, 2393

Offset: 1

Author

Jack Braxton, Apr 05 2023

Keywords

• nonn

Comments

All terms are prime because all terms in A362034 are.

Examples

			2 is a term because in A362034, 2 occurs at positions 1, 2, and 3.
17 is a term because in A362034, 17 occurs at positions 13, 23, and 27.
		

Crossrefs

Cf. A000040, A362034.

Programs

Mathematica

nn = 300; q = Prime[nn]; c[] = 0; p[] = False; T[n_, 0] := T[n, n] = 2; T[n_, k_] := T[n, k] = NextPrime[T[n - 1, k - 1] + T[n - 1, k] - 1]; TakeWhile[Sort@ Reap[Do[(c[#]++; If[And[c[#] >= 3, ! p[#]], Sow[#]; p[#] = True]) &@ T[n, k], {n, 0, nn}, {k, 0, n}] ][[-1, -1]], # <= q &] (* Michael De Vlieger, Apr 06 2023 *)