A176584 Primes of the form p = k^3 + (largest square <= k^3).

2, 194057, 601067, 1607173, 3283993, 3630257, 3721363, 4918999, 5255713, 5848307, 6749569, 9999907, 17992913, 20432729, 23393483, 34746203, 44845993, 73843813, 84277273, 107165033, 109735649, 120469409, 125138873, 130898927

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Keywords

• nonn

Comments

Consider k = 4 * x^2 + 1, where the largest square <= k^3 is (8 * x^3 + 3 * x)^2. Bunyakowsky's conjecture implies there are infinitely many primes of the form (4 * x^2 + 1)^3 + (8 * x^3 + 3 * x)^2, and so that the sequence is infinite. The first term of this form is 93389778901 = a(165), corresponding to x = 30. - Robert Israel, Jan 10 2024

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Primes in A176580.

Cf. A065733, A075847, A077116, A176581, A176582, A176583.

Programs

Maple

g:= n -> n + floor(sqrt(n))^2:
select(isprime,map(g,[seq(i^3,i=1..1000)])); # Robert Israel, Jan 10 2024

Mathematica

r[n_]:=n^3;f[n_]:=r[n]+Floor[Sqrt[r[n]]]^2;Select[Table[f[n],{n,0,6!}],PrimeQ[ # ]&]

PARI

select(isprime, vector(1000, n, n^3+sqrtint(n^3)^2)) \\ Michel Marcus, Jan 10 2024