A206606 Primes that can be written as a sum of a positive square and a positive cube in more than two ways.

2089, 4481, 7057, 15193, 15641, 16649, 23417, 34721, 65537, 68489, 69697, 72577, 93241, 118673, 123209, 146161, 173897, 176401, 191969, 199873, 205721, 216233, 239633, 259121, 264169, 271169, 280009, 286289, 296353, 301409, 318313, 342233, 347993, 357569, 381529, 447569, 466273, 477577, 526249, 534577

Offset

1,1

Comments

A subset of these, {65537, 93241, 191969, ..} allows this representation in more than 3 ways.

Links

Robert Israel, Table of n, a(n) for n = 1..3930

Example

2089 = 19^2+12^3 = 33^2+10^3 = 45^2+4^3

Maple

N:= 10^6: # to get all terms <= N
for x from 1 to floor(N^(1/2)) do
  for y from 1 to floor((N-x^2)^(1/3)) do
    p:= x^2 + y^3;
    if isprime(p) then
      if assigned(R[p]) then R[p]:= R[p]+1
      else R[p]:= 1
      fi
    fi
  od
od:
sort(map(op, select(t -> R[op(t)]>2, [indices(R)]))); # Robert Israel, Mar 21 2017

Mathematica

t={}; Do[Do[AppendTo[t, n^2+m^3], {n, 300}], {m, 300}]; t=Sort[t]; t3={}; Do[If[t[[n]]==t[[n+2]]&&PrimeQ[t[[n]]], AppendTo[t3, t[[n]]]], {n, Length[t]-2}]; t3; f1[l_]:=Module[{t={}}, Do[If[l[[n]]!=l[[n+1]], AppendTo[t, l[[n]]]], {n, Length[l]-1}]; t]; (*ExtractSingleTermsOnly*) f1[t3] (* or *)
mx = 10^6; First /@ Sort@ Select[ Tally[ Join @@ Reap[(Sow@ Select[#^3 + Range[ Sqrt[mx - #^3]]^2, PrimeQ]) & /@ Range[mx^(1/3)]][[2, 1]]], #[[2]]>2 &] (* faster, Giovanni Resta, Mar 21 2017 *)

Crossrefs

Cf. A054402, A123364, A162930

Sequence in context: A221360 A106720 A179124 * A089159 A045051 A102504

Adjacent sequences: A206603 A206604 A206605 * A206607 A206608 A206609

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 10 2012

Extensions

More terms from Robert Israel, Mar 21 2017

Status

approved