A280828 Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

4, 22, 202

Offset: 1

Author

Sergey Pavlov, Jan 08 2017

Keywords

• nonn
• hard
• bref
• more

Comments

Let k=2*10^(n-1)+2, then a(n)=10^k+9. For all k>4, k is a term of A058441.

The only known terms from A088275 (Numbers n such that 10^n + 9 is prime) that are of the form 2*10^j + 2 are 4, 22, and 202; given the lower bound given for that sequence's next term, a(4) >= 200002. - Jon E. Schoenfield, Jan 11 2017

For n<4, let k=a(n) and p=(10^k-9)/10^(k/2)+3=10^(k/2)+3, then p is prime. - Sergey Pavlov, Jan 13 2017

Examples

			For n=1, a(1)=4 and 10^4 + 9 is prime.
		

Crossrefs

Cf. A043037, A058441, A088275, A144249, A205529.

Formula

Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.