A261459 Numbers k such that the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's is prime.

1, 3, 4, 5, 6, 10, 254, 410, 751, 1101, 2488, 3476, 14124, 20060

Offset: 1

Author

Chai Wah Wu, Oct 19 2015

Keywords

• nonn
• base
• more

Comments

Numbers k that generate the terms in A263299.

a(13) > 10000 if it exists. - Chai Wah Wu, Oct 22 2015

Crossrefs

Cf. A263299.

Programs

PARI

for(n=1, 1e3, if(isprime(eval(Str((10^n - 1)/9, n^2 + n + 1, (10^n - 1)/9))), print1(n", "))); \\ Altug Alkan, Oct 20 2015

Python

from gmpy2 import is_prime
A261459_list = [k for k in range(10**3) if is_prime(int('1'*k+str(k*(k+1)+1)+'1'*k))]

Extensions

a(13)-a(14) from Michael S. Branicky, Jun 06 2023