|
%I #22 Dec 18 2018 18:01:04
%S 12,17,31,33,36,52,57,76,129,134,148,150,174,177,196,246,294,297,316,
%T 347,352,368,369,388,392,414,464,486,512,537,556,632,654,704,849,868,
%U 872,966,969,988,1086,1184,1304,1335,1340,1356,1377,1380,1396,1452
%N Numbers of the form p^2 + q^3, p,q prime.
%H Ray Chandler, <a href="/A045699/b045699.txt">Table of n, a(n) for n = 1..10000</a>
%F Numbers n such that A045701(n)>0.
%e a(4)=36 because 36=3^3+3^2; a(7)=76 because 76=3^3+7^2.
%t max = 1500; pp = Prime[Range[PrimePi[Sqrt[max]]]]; qq = Prime[Range[PrimePi[max^(1/3)]]]; Select[Union[Flatten[Outer[Plus, pp^2, qq^3]]], # <= max&] (* _Jean-François Alcover_, Apr 26 2011 *)
%t With[{upto=1500},Select[Union[Flatten[{#[[1]]^2+#[[2]]^3,#[[2]]^2+ #[[1]]^3}&/@ Tuples[Prime[Range[Floor[Sqrt[upto/8]]]],2]]],#<=upto&]] (* _Harvey P. Dale_, Dec 18 2018 *)
%o (PARI) list(lim)=my(v=List(),t); lim\=1; forprime(q=2,sqrtnint(lim-4,3), t=q^3; forprime(p=2,sqrtint(lim-t), listput(v, p^2+t))); Set(v) \\ _Charles R Greathouse IV_, Jun 07 2016
%Y Cf. A000040, A045700, A196752, A196753.
%K nonn,nice
%O 1,1
%A _Felice Russo_
|
