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Numbers n such that 10^(2n+1) + 21*10^n + 1 is prime.
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%I #26 Jul 10 2015 18:03:01

%S 2,3,11,12,15,42,311,314,579,1943,2262,5199,7329,12792

%N Numbers n such that 10^(2n+1) + 21*10^n + 1 is prime.

%C This is the analog of A096594, the numbers n for which the concatenation of 10^n and 10^n - 1 is prime, with the numbers concatenated here being 10^n + 2 and 10^n + 1. For example, 3 is in this sequence because 10021001 is prime, and 3 is in A096594 since 1000999 is prime.

%C All the primes arising from terms up to a(14) have been certified with pfgw. a(15) > 32400. - _Giovanni Resta_, Feb 18 2013

%e 1 is not in the sequence since 10^(2*1+1) + 21*10^1 + 1 = 1000 + 210 + 1 = 1211 is composite.

%e 2 is in the sequence since 10^(2*2+1) + 21*10^2 + 1 = 100000 + 2100 + 1 = 102101 is prime.

%t Select[Range[500], PrimeQ[10^(2# + 1) + 21 * 10^# + 1] &] (* _Alonso del Arte_, Feb 17 2013 *)

%o (PARI) i=1; while(1, if(ispseudoprime(10^(2*i+1) + 21*10^i + 1), print1("\n"i"\n")); if(i%10==0, print1("*")); i++; next())

%Y Cf. A096594.

%K nonn,base

%O 1,1

%A _James G. Merickel_, Feb 13 2013

%E a(14) from _Giovanni Resta_, Feb 18 2013