A066649 Primes of the form a^2 + b^3 with a, b > 0.

2, 5, 17, 31, 37, 43, 73, 89, 101, 113, 127, 197, 223, 233, 241, 257, 269, 283, 337, 347, 353, 359, 379, 401, 443, 449, 487, 521, 577, 593, 599, 677, 701, 733, 743, 811, 827, 829, 919, 953, 1009, 1019, 1049, 1051, 1097, 1129, 1153, 1213, 1289, 1297, 1361

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Jori Merikoski, On primes represented by aX^2+bY^3aX^2+bY^3, arXiv preprint (2025). arXiv:2503.05396 [math.NT]

Formula

On Conjecture C_a(1/17), this sequence is infinite and a(n) << n^(6/5) log n, see Merikoski link. - Charles R Greathouse IV, Mar 11 2025

Example

A000040(26) = 101 = 10^2 + 1^3, therefore 101 is a term.
A000040(51) = a(13) = 233 = 225 + 8 = 15^2 + 2^3.

Mathematica

lst={}; Do[Do[p=n^2+m^3; If[PrimeQ[p], AppendTo[lst, p]], {n, 5!}], {m, 5!}]; Take[Union[lst], 123] (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)

Prog

(PARI) list(lim)=my(v=List()); for(y=1, sqrtnint(lim\=1, 3), my(y3=y^3); for(x=1, sqrtint(lim-y3), my(p=y3+x^2); if(isprime(p), listput(v, p)))); Set(v) \\ Charles R Greathouse IV, Mar 11 2025

Crossrefs

Cf. A055394, A066650.

Cf. A000040, A078393, A078390.

Sequence in context: A172122 A101009 A269018 * A075345 A045705 A125822

Adjacent sequences: A066646 A066647 A066648 * A066650 A066651 A066652

Keyword

nonn,changed

Author

Reinhard Zumkeller, Dec 17 2001

Status

approved