

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.


1



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

1,1


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^p1) is a prime number (a(10^(p1)) 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)


LINKS

Table of n, a(n) for n=1..21.


EXAMPLE

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


CROSSREFS

Cf. A086766, A252491.
Sequence in context: A078271 A272617 A301473 * A085878 A238633 A266815
Adjacent sequences: A087400 A087401 A087402 * A087404 A087405 A087406


KEYWORD

base,nonn


AUTHOR

Amarnath Murthy, Sep 10 2003


STATUS

approved



