A376933 a(n) = (A376907(n) - 10^(n-1))/3.

2, 3, 9, 219, 89, 707, 7139, 17397, 127107, 185573, 170099, 8513673, 3730629, 9645947, 20878187, 435128997, 413502597, 7180622897, 28071202809, 4197184407, 53159437779, 72827487477, 408466487673, 1622948986427, 1009480191957, 50924645281527, 141362538039039

Offset: 1

Author

Stefano Spezia, Oct 11 2024

Keywords

• nonn
• base

Crossrefs

Cf. A011557, A376907.

Programs

Mathematica

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

PARI

a(n) = my(m=10^(n-1), p); for(k=(sqrtint(12*m-3)-3)\6, oo, p=3*k*(k+1)+1; if(p>m&&isprime(p), return((p-m)/3))); \\ Jinyuan Wang, Mar 01 2025

Python

from itertools import count
from math import isqrt
from sympy import isprime
def A376933(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-a)//3 # Chai Wah Wu, Oct 13 2024

Extensions

a(21)-a(27) from Chai Wah Wu, Oct 13 2024