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A214511 Least number having n orderless representations as p^2 + q^2, where p and q are primes. 10

%I

%S 8,338,2210,10370,202130,229970,197210,81770,18423410,16046810,

%T 12625730,21899930,9549410,370247930,416392730,579994610,338609570,

%U 2155919090,601741010,254885930,10083683090,4690939370,29207671610,30431277890,22264417370,23231920010

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

%C A045698(a(n)) = n and A045698(m) < n for m < a(n). - _Reinhard Zumkeller_, Jul 29 2012

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

%H Giovanni Resta, <a href="/A214511/b214511.txt">Table of n, a(n) for n = 1..51</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

%t 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]]

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a214511 = (+ 1) . fromJust . (`elemIndex` a045698_list)

%o -- _Reinhard Zumkeller_, Jul 29 2012

%Y Cf. A088919, A045636, A214723.

%Y Cf. A016032 (p and q integers).

%Y Cf. A214512, A214513.

%K nonn

%O 1,1

%A _T. D. Noe_, Jul 26 2012

%E a(21)-a(26) from _Donovan Johnson_, Jul 29 2012

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)