A077116 -id:A077116 - cp's OEIS frontend

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

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

nonn

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

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

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 *)

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

A198831 Successive records in maximal positive distance d = x^3 - y^2.

Original entry on oeis.org

0, 4, 20, 28, 39, 47, 81, 135, 152, 207, 216, 270, 496, 546, 615, 732, 832, 1148, 1208, 1343, 1391, 1541, 1750, 2000, 2260, 2548, 2575, 2825, 3679, 3807, 4220, 4604, 5076, 5508, 5835, 5859, 6291, 7538, 7656, 8188, 8423, 8712, 8964, 12092, 12205, 12511, 12926

Offset: 1

Artur Jasinski, Oct 30 2011

nonn

Successive records in A077116.

J. Calvo, J. Herranz, G. Saez, A new algorithm to search for small nonzero |x^3 - y^2| values, Math. Comp. 78 (2009), 2435-2444.

Cf. A077116, A078933, A179107, A179108, A179109.

aa = {}; bb = {}; max = -1; Do[kk = x^3 - Floor[x^(3/2)]^2; If[kk > max, AppendTo[aa, kk]; AppendTo[bb, x]; max = kk], {x, 1, 10000}]; aa

cp's OEIS Frontend

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

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