A094714 Smallest prime having exactly n representations as a^2+b^2+c^2 with c >= b >= a > 0.

2, 3, 41, 89, 251, 269, 593, 461, 521, 929, 761, 941, 1109, 1481, 1601, 1361, 2309, 1949, 1889, 2141, 2729, 2609, 3701, 3461, 3989, 3449, 5309, 4241, 4289, 5081, 7589, 5381, 9521, 6569, 8861, 7229, 7829, 8501, 8069, 13781, 8609, 12689, 10601, 11261, 14741

Offset

0,1

Links

Donovan Johnson, Table of n, a(n) for n = 0..5000

Example

a(2) = 41 because 41 = 1+4+36 = 9+16+16.
a(2^10) = a(1024) = 3521909 = prime(251585). - Zak Seidov, Nov 10 2013

Mathematica

lim=50; pLst=Table[0, {PrimePi[lim^2]}]; Do[n=a^2+b^2+c^2; If[n<lim^2 && PrimeQ[n], pLst[[PrimePi[n]]]++ ], {a, lim}, {b, a, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}; Table[First[Prime[Flatten[Position[pLst, n]]]], {n, 0, 38}]

Crossrefs

Cf. A094713 (number of ways that prime(n) can be represented as a^2+b^2+c^2 with a >= b >= c > 0).

Sequence in context: A215154 A215101 A377791 * A200817 A042475 A241277

Adjacent sequences: A094711 A094712 A094713 * A094715 A094716 A094717

Keyword

nonn

Author

T. D. Noe, May 21 2004

Status

approved