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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 (list; graph; refs; listen; history; text; internal format)
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^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)

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

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Last modified September 16 18:24 EDT 2019. Contains 327116 sequences. (Running on oeis4.)