A223705 Least number k such that prime(n) is the largest divisor of k^2 + 1, or 0 if there is no such k.

1, 0, 2, 0, 0, 5, 4, 0, 0, 12, 0, 6, 9, 0, 0, 23, 0, 11, 0, 0, 27, 0, 0, 34, 22, 10, 0, 0, 33, 15, 0, 0, 37, 0, 44, 0, 28, 0, 0, 80, 0, 19, 0, 81, 14, 0, 0, 0, 0, 107, 89, 0, 64, 0, 16, 0, 82, 0, 60, 53, 0, 138, 0, 0, 25, 114, 0, 148, 0, 136, 42, 0, 0, 104, 0, 0

Offset: 1

Author

T. D. Noe, Apr 03 2013

Keywords

• nonn

Comments

Note that a(n) = 0 for prime(n) = 3 (mod 4). If the zeros are removed, A002314 (with 1 prepended) and A177979 are produced.

Crossrefs

Cf. A223701-A223707 (related sequences).

Programs

Mathematica

nn = 100; t = Table[0, {nn}]; Do[If[Mod[Prime[n], 4] == 3, t[[n]] = -1], {n, nn}]; n = 0; While[Times @@ t == 0, n++; s = FactorInteger[n^2 + 1][[-1, 1]]; p = PrimePi[s]; If[p <= nn && t[[p]] == 0, t[[p]] = n]]; Do[If[Mod[Prime[n], 4] == 3, t[[n]] = 0], {n, nn}]; t