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A376907
a(n) is the least n-digit cuban prime.
3
7, 19, 127, 1657, 10267, 102121, 1021417, 10052191, 100381321, 1000556719, 10000510297, 100025541019, 1000011191887, 10000028937841, 100000062634561, 1000001305386991, 10000001240507791, 100000021541868691, 1000000084213608427, 10000000012591553221, 100000000159478313337
OFFSET
1,1
COMMENTS
a(n) - A011557(n-1) is a multiple of 3.
LINKS
FORMULA
Conjecture: a(n+1)/a(n) ~ 10.
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]<n, k++]; m]; Array[a, 15]
PROG
(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
KEYWORD
nonn,base
AUTHOR
Stefano Spezia, Oct 08 2024
STATUS
approved