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

1,3

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.

Links

Table of n, a(n) for n=1..76.

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

Crossrefs

Cf. A223701-A223707 (related sequences).

Sequence in context: A324040 A340116 A361521 * A358304 A285192 A278177

Adjacent sequences: A223702 A223703 A223704 * A223706 A223707 A223708

Keyword

nonn

Author

T. D. Noe, Apr 03 2013

Status

approved