login
The OEIS is supported by the many generous donors 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. 3
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
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
Sequence in context: A221360 A106720 A179124 * A089159 A045051 A102504
KEYWORD
nonn
AUTHOR
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)