login
A214511
Least number having n orderless representations as p^2 + q^2, where p and q are primes.
10
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
1,1
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
EXAMPLE
a(2) = 338 because 338 = 7^2 + 17^2 = 13^2 + 13^2 and 338 is the least number with this property.
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]]
PROG
(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a214511 = (+ 1) . fromJust . (`elemIndex` a045698_list)
-- Reinhard Zumkeller, Jul 29 2012
CROSSREFS
Cf. A016032 (p and q integers).
Sequence in context: A247730 A258745 A071306 * A117082 A061458 A135067
KEYWORD
nonn
AUTHOR
T. D. Noe, Jul 26 2012
EXTENSIONS
a(21)-a(26) from Donovan Johnson, Jul 29 2012
STATUS
approved