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

%I A206606 #12 Mar 22 2017 00:26:11
%S A206606 2089,4481,7057,15193,15641,16649,23417,34721,65537,68489,69697,72577,
%T A206606 93241,118673,123209,146161,173897,176401,191969,199873,205721,216233,
%U A206606 239633,259121,264169,271169,280009,286289,296353,301409,318313,342233,347993,357569,381529,447569,466273,477577,526249,534577
%N A206606 Primes that can be written as a sum of a positive square and a positive cube in more than two ways.
%C A206606 A subset of these, {65537, 93241, 191969, ..} allows this representation in more than 3 ways.
%H A206606 Robert Israel, <a href="/A206606/b206606.txt">Table of n, a(n) for n = 1..3930</a>
%e A206606 2089 = 19^2+12^3 = 33^2+10^3 = 45^2+4^3
%p A206606 N:= 10^6: # to get all terms <= N
%p A206606 for x from 1 to floor(N^(1/2)) do
%p A206606   for y from 1 to floor((N-x^2)^(1/3)) do
%p A206606     p:= x^2 + y^3;
%p A206606     if isprime(p) then
%p A206606       if assigned(R[p]) then R[p]:= R[p]+1
%p A206606       else R[p]:= 1
%p A206606       fi
%p A206606     fi
%p A206606   od
%p A206606 od:
%p A206606 sort(map(op,select(t -> R[op(t)]>2, [indices(R)]))); # _Robert Israel_, Mar 21 2017
%t A206606 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 *)
%t A206606 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 *)
%Y A206606 Cf. A054402, A123364, A162930
%K A206606 nonn
%O A206606 1,1
%A A206606 _Vladimir Joseph Stephan Orlovsky_, Feb 10 2012
%E A206606 More terms from _Robert Israel_, Mar 21 2017