A376907 a(n) is the least n-digit cuban prime.

7, 19, 127, 1657, 10267, 102121, 1021417, 10052191, 100381321, 1000556719, 10000510297, 100025541019, 1000011191887, 10000028937841, 100000062634561, 1000001305386991, 10000001240507791, 100000021541868691, 1000000084213608427, 10000000012591553221, 100000000159478313337

Offset: 1

Author

Stefano Spezia, Oct 08 2024

Keywords

• nonn
• base

Comments

a(n) - A011557(n-1) is a multiple of 3.

Links

• Robert Israel, Table of n, a(n) for n = 1..996

Crossrefs

Cf. A002407, A003215, A003617, A011557, A111251, A113478, A145203, A376933.

Programs

Maple

nextcuban:= proc(n)
  local k,y;
  for k from ceil((sqrt(12*n-3)-3)/6) do
    y:= (k+1)^3 - k^3;
    if isprime(y) then return y fi
  od
end proc:
seq(nextcuban(10^i), i = 0 .. 25); # Robert Israel, Nov 08 2024

Mathematica

a[n_]:=Module[{k=1},While[!PrimeQ[m=3k^2+3k+1]||IntegerLength[m]
				

Python

from itertools import count
from math import isqrt
from sympy import isprime
def A376907(n):
    for k in count(isqrt((((a:=10**(n-1))<<2)-1)//12)):
        m = 3*k*(k+1)+1
        if m >= a and isprime(m):
            return m # Chai Wah Wu, Oct 13 2024

Formula

Conjecture: a(n+1)/a(n) ~ 10.