A212129 Numbers n such that 10^(2n+1) + 21*10^n + 1 is prime.

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

Offset: 1

Author

James G. Merickel, Feb 13 2013

Keywords

• nonn
• base

Comments

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.

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

Examples

			1 is not in the sequence since 10^(2*1+1) + 21*10^1 + 1 = 1000 + 210 + 1 = 1211 is composite.
2 is in the sequence since 10^(2*2+1) + 21*10^2 + 1 = 100000 + 2100 + 1 = 102101 is prime.
		

Crossrefs

Cf. A096594.

Programs

Mathematica

Select[Range[500], PrimeQ[10^(2# + 1) + 21 * 10^# + 1] &] (* Alonso del Arte, Feb 17 2013 *)

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())

Extensions

a(14) from Giovanni Resta, Feb 18 2013