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A214723 Numbers of the form p^2 + q^2, with p and q prime, in exactly one way. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A070130 A070131

Adjacent sequences:  A214720 A214721 A214722 * A214724 A214725 A214726

KEYWORD

nonn

AUTHOR

J. Stauduhar, Jul 26 2012

STATUS

approved

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Last modified June 13 10:36 EDT 2021. Contains 344988 sequences. (Running on oeis4.)