A094714 - OEIS

A094714

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

%I #12 Nov 16 2013 14:18:03

%S 2,3,41,89,251,269,593,461,521,929,761,941,1109,1481,1601,1361,2309,

%T 1949,1889,2141,2729,2609,3701,3461,3989,3449,5309,4241,4289,5081,

%U 7589,5381,9521,6569,8861,7229,7829,8501,8069,13781,8609,12689,10601,11261,14741

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

%H Donovan Johnson, <a href="/A094714/b094714.txt">Table of n, a(n) for n = 0..5000</a>

%e a(2) = 41 because 41 = 1+4+36 = 9+16+16.

%e a(2^10) = a(1024) = 3521909 = prime(251585). - _Zak Seidov_, Nov 10 2013

%t 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}]

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

%K nonn

%O 0,1

%A _T. D. Noe_, May 21 2004