login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(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
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 (list; graph; refs; listen; history; text; internal format)
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

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 November 16 22:20 EST 2019. Contains 329208 sequences. (Running on oeis4.)