This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A206606 Primes that can be written as a sum of a positive square and a positive cube in more than two ways. 2


%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]]>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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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