A214511 Least number having n orderless representations as p^2 + q^2, where p and q are primes.

8, 338, 2210, 10370, 202130, 229970, 197210, 81770, 18423410, 16046810, 12625730, 21899930, 9549410, 370247930, 416392730, 579994610, 338609570, 2155919090, 601741010, 254885930, 10083683090, 4690939370, 29207671610, 30431277890, 22264417370, 23231920010

Offset: 1

Author

T. D. Noe, Jul 26 2012

Keywords

• nonn

Comments

A045698(a(n)) = n and A045698(m) < n for m < a(n). - Reinhard Zumkeller, Jul 29 2012

a(53) = 3374376505370. a(52) and terms following a(53) are greater than 4*10^13. - Giovanni Resta, Jul 02 2018

Examples

			a(2) = 338 because 338 = 7^2 + 17^2 = 13^2 + 13^2 and 338 is the least number with this property.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..51
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A088919, A045636, A214723.

Cf. A016032 (p and q integers).

Cf. A214512, A214513.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a214511 = (+ 1) . fromJust . (`elemIndex` a045698_list)
-- Reinhard Zumkeller, Jul 29 2012

Mathematica

nn = 10^6; 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 &]; 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]]

Extensions

a(21)-a(26) from Donovan Johnson, Jul 29 2012