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

%I

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

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

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

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

%p 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

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

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

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

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

%K nonn,more,base,hard

%O 1,2

%A _Serge Batalov_, Nov 16 2014

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)