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Numbers k such that the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's is prime.
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%I #19 Jun 07 2023 08:49:09

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

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

%C Numbers k that generate the terms in A263299.

%C a(13) > 10000 if it exists. - _Chai Wah Wu_, Oct 22 2015

%o (Python)

%o from gmpy2 import is_prime

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

%o (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

%Y Cf. A263299.

%K nonn,base,more

%O 1,2

%A _Chai Wah Wu_, Oct 19 2015

%E a(13)-a(14) from _Michael S. Branicky_, Jun 06 2023