A087403 a(n) = smallest prime of the form 10*K(n) + 1, where K is a number obtained by concatenation of n with itself, or 0 if no such prime exists.

11, 2221, 31, 41, 555555555551, 61, 71, 881, 991, 101, 1111111111111111111, 1212121, 131, 14141414141, 151, 1616161, 1717171717171717171717171717171, 181, 191, 20201, 211

Offset: 1

Author

Amarnath Murthy, Sep 10 2003

Keywords

• base
• nonn

Comments

Conjecture: No term is zero.

Next term a(22) is too large (121 digits) to include in sequence. - Ray Chandler, Sep 23 2003

From Farideh Firoozbakht, Jan 07 2015: (Start)

The conjecture is not true. There exist many numbers n such that a(n)=0.

By using the theorem and its corollary mentioned in the comments lines of the sequence A086766, we can prove that for m = 2, 3, ..., 275 a(10^m)=0.

What is the smallest odd prime p, such that (10^(p^2)-1)/(10^p-1) is a prime number (a(10^(p-1)) is nonzero)?

What is the smallest integer m, such that m > 1 and a(10^m) is nonzero?

Conjecture: If n is not of the form 10^m then a(n) is nonzero.

(End)

Examples

			a(2) = 2221 is a prime but 21 and 221 are composite.
		

Crossrefs

Cf. A086766, A252491.