A176586 Primes of the form : n^3 + Largest square + Smallest square, (Largest square <= n^3, Smallest square >= n^3).

3, 222601, 2824933, 3573761, 4215749, 5183821, 6001997, 6592613, 7886597, 8592401, 9725393, 10127813, 10531813, 12751093, 13720661, 15263009, 18087529, 30232597, 52730113, 68727469, 79395353, 109787269, 139967461, 162040453

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

r[n_]:=n^3; f[n_]:=r[n]+Floor[Sqrt[r[n]]]^2+Ceiling[Sqrt[r[n]]]^2; Select[Table[f[n], {n, 0, 7!}], PrimeQ[ # ]&]
lsss[n_]:=Module[{c=n^3}, c+Floor[Sqrt[c]]^2+Ceiling[Sqrt[c]]^2]; Select[Array[ lsss, 1000], PrimeQ] (* Harvey P. Dale, Feb 22 2023 *)

Prog

(PARI) print1(3); for(n=2, 1e3, t=sqrtint(n^3); if(isprime(t=n^3+t^2+ (t+1)^2) && !issquare(n), print1(", "t))) \\ Charles R Greathouse IV, Apr 15 2012

Crossrefs

Cf. A065733, A075847, A077116, A176580, A176581, A176582, A176583, A176584, A176585.

Sequence in context: A003544 A250495 A317168 * A339776 A033982 A326618

Adjacent sequences: A176583 A176584 A176585 * A176587 A176588 A176589

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Status

approved