A214723 Numbers of the form p^2 + q^2, with p and q prime, in exactly one way.

8, 13, 18, 29, 34, 50, 53, 58, 74, 98, 125, 130, 146, 170, 173, 178, 194, 218, 242, 290, 293, 298, 314, 365, 370, 386, 458, 482, 530, 533, 538, 554, 698, 722, 818, 845, 850, 866, 962, 965, 970, 986, 1058, 1082, 1202, 1250, 1322, 1370, 1373, 1378, 1394, 1418

Offset: 1

Author

J. Stauduhar, Jul 26 2012

Keywords

• nonn

Comments

A045698(a(n)) = 1. - Reinhard Zumkeller, Jul 29 2012

Examples

			a(1) = 8 = 2^2 + 2^2, and no other p^2 + q^2 sums to 8.
Both 7^2 + 17^2 and 13^2 + 13^2 sum to 338, so 338 is not in this sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to sums of squares

Crossrefs

Subsequence of A045636 (numbers of the form p^2 + q^2).

Programs

Haskell

import Data.List (elemIndices)
a214723 n = a214723_list !! (n-1)
a214723_list = elemIndices 1 a045698_list
-- Reinhard Zumkeller, Jul 29 2012

Mathematica

nn = 2000; ps = Prime[Range[PrimePi[Sqrt[nn]]]]; t = Flatten[Table[ps[[i]]^2 + ps[[j]]^2, {i, Length[ps]}, {j, i, Length[ps]}]]; t = Select[t, # <= nn &]; Sort[Transpose[Select[Tally[t], #[[2]] == 1 &]][[1]]] (* T. D. Noe, Jul 26 2012 *)