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

1,1

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for sequences related to sums of squares

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A006619 A023487 A045636 * A022954 A364411 A359853

Adjacent sequences: A214720 A214721 A214722 * A214724 A214725 A214726

Keyword

nonn

Author

J. Stauduhar, Jul 26 2012

Status

approved