A214513 Least number having n orderless representations as p^2 + q^2 + r^2 + s^2, where p, q, r, and s are primes.

16, 148, 196, 436, 388, 628, 868, 988, 1228, 1468, 1708, 2212, 2068, 2860, 2620, 2380, 3220, 3388, 3700, 4108, 3940, 4180, 5260, 4228, 5068, 4900, 5500, 6220, 6340, 7780, 5908, 5740, 6580, 7540, 8260, 7420, 8860, 9340, 11260, 10708, 9940, 9100, 10180, 12820

Offset: 1

Author

T. D. Noe, Jul 29 2012

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A025416, A025417, A214511, A214512.

Programs

Mathematica

nn = 10^5; ps = Prime[Range[PrimePi[Sqrt[nn]]]]; t = Flatten[Table[ps[[i]]^2 + ps[[j]]^2 + ps[[k]]^2 + ps[[l]]^2, {i, Length[ps]}, {j, i, Length[ps]}, {k, j, Length[ps]}, {l, k, Length[ps]}]]; t = Select[t, # <= nn &]; t2 = Sort[Tally[t]]; u = Union[Transpose[t2][[2]]]; d = Complement[Range[u[[-1]]], u]; If[d == {}, nLim = u[[-1]], nLim = d[[1]]-1]; t3 = Table[Select[t2, #[[2]] == n &, 1][[1]], {n, nLim}]; Transpose[t3][[1]]