A246804 Numbers k such that (10^(k+2) + 999) * 10^k + 1 is prime.

1, 3, 15, 135, 645, 1373, 195317, 237249

Offset: 1

Author

Serge Batalov, Nov 16 2014

Keywords

• nonn
• more
• base
• hard

Comments

Or, indices of primes in the sequence of decimal palindromes 19991, 1099901, 100999001, 10009990001, ...

Or, numbers k such that there exists an "upside-down-Belphegor's primes" of length 2*k+3.

Crossrefs

Cf. A156166 (Belphegor's primes), A082703 (plateau primes 199...991).

Programs

Magma

[n: n in [1..500] | IsPrime((10^(n+2)+999)*10^n+1)];

Maple

A246804:=n->`if`(isprime((10^(n+2)+999)*10^n+1), n, NULL): seq(A246804(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014

Mathematica

Select[Range[10^3], PrimeQ[(10^(# + 2) + 999)*10^# + 1] &]

PARI

for( n=1,9999, ispseudoprime((10^(n+2)+999)*10^n+1) & print1(n","))