A376933 -id:A376933 - cp's OEIS frontend

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

Stefano Spezia, Oct 08 2024

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

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

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

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

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

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

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

A376993 a(n) = A376992(n) - 10^(n-1).

Original entry on oeis.org

4, 3, 13, 13, 513, 801, 6781, 30721, 40513, 1057513, 515313, 16728501, 78402181, 13617661, 472012281, 64846161, 5481873013, 2459693601, 116852093013, 62611784481, 1234170737761, 1565435686113, 17492477581161, 2254878102513, 16836143444113, 229959946206301

Offset: 1

Stefano Spezia, Oct 11 2024

Cf. A011557, A376933, A376992.

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

from math import isqrt
from itertools import count
from sympy import isprime
def A376993(n):
    for k in count(isqrt(((a:=10**(n-1))<<1)-1>>2)):
        m = 2*k*(k+1)+1
        if m >= a and isprime(m):
            return m-a # Chai Wah Wu, Oct 13 2024

a(21)-a(26) from Chai Wah Wu, Oct 13 2024

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula