A077037 Largest prime < n^3.

7, 23, 61, 113, 211, 337, 509, 727, 997, 1327, 1723, 2179, 2741, 3373, 4093, 4909, 5827, 6857, 7993, 9257, 10639, 12163, 13807, 15619, 17573, 19681, 21943, 24379, 26993, 29789, 32749, 35933, 39301, 42863, 46649, 50651, 54869, 59281, 63997

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Formula

a(n) > (n-1)^3 for all large n, by Ingham's theorem (see A060199). - Jonathan Sondow, Mar 27 2014

Mathematica

PrimePrev[n_]:=Module[{k}, k=n-1; While[ !PrimeQ[k], k-- ]; k]; f[n_]:=n^3; lst={}; Do[AppendTo[lst, PrimePrev[f[n]]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
Table[NextPrime[n^3, -1], {n, 2, 40}] (* Robert G. Wilson v, Aug 17 2010 *)

Prog

(Python)
from sympy import prevprime
def a(n):  return prevprime(n**3)
print([a(n) for n in range(2, 41)]) # Michael S. Branicky, Jul 23 2021
(PARI) a(n) = precprime(n^3); \\ Michel Marcus, Jan 14 2023

Crossrefs

Cf. A053001, A014220, A000578, A060199.

Sequence in context: A140096 A096345 A211644 * A201110 A333187 A220509

Adjacent sequences: A077034 A077035 A077036 * A077038 A077039 A077040

Keyword

nonn

Author

Reinhard Zumkeller, Oct 21 2002

Status

approved