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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. 2

%I

%S 2089,4481,7057,15193,15641,16649,23417,34721,65537,68489,69697,72577,

%T 93241,118673,123209,146161,173897,176401,191969,199873,205721,216233,

%U 239633,259121,264169,271169,280009,286289,296353,301409,318313,342233,347993,357569,381529,447569,466273,477577,526249,534577

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

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

%H Robert Israel, <a href="/A206606/b206606.txt">Table of n, a(n) for n = 1..3930</a>

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

%p N:= 10^6: # to get all terms <= N

%p for x from 1 to floor(N^(1/2)) do

%p for y from 1 to floor((N-x^2)^(1/3)) do

%p p:= x^2 + y^3;

%p if isprime(p) then

%p if assigned(R[p]) then R[p]:= R[p]+1

%p else R[p]:= 1

%p fi

%p fi

%p od

%p od:

%p sort(map(op,select(t -> R[op(t)]>2, [indices(R)]))); # _Robert Israel_, Mar 21 2017

%t 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 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 &] (* faster, _Giovanni Resta_, Mar 21 2017 *)

%Y Cf. A054402, A123364, A162930

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 10 2012

%E More terms from _Robert Israel_, Mar 21 2017

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Last modified December 6 07:05 EST 2019. Contains 329784 sequences. (Running on oeis4.)