

A156166


Numbers k > 0 such that (10^(k+2) + 666)*10^k + 1 is prime.


4




OFFSET

1,2


COMMENTS

Or, indices of primes in the sequence 16661, 1066601, 100666001, 10006660001,... Ondrejka calls these "beastly palindromic primes".
In popular culture: the number generated by a(2), 1000000000000066600000000000001, also known as Belphegor's Prime, was used as a plot device in Episode "Just a Regular Irregular" of the "Elementary" TV series (first aired Nov/13/2014).  Serge Batalov, Nov 15 2014


LINKS

Table of n, a(n) for n=1..9.
C. Caldwell, H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), p. 32
Internet Movie Database, Elementary: Season 3, Episode 3: Just a Regular Irregular
Clifford A. Pickover, Belphegor's Prime: 1000000000000066600000000000001
Eric Weisstein's World of Mathematics, Belphegor Prime
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Wikipedia, Belphegor's prime


FORMULA

a(n) = A232448(n) + 1.


MAPLE

A156166:=n>`if`(isprime((10^(n+2)+666)*10^n+1), n, NULL): seq(A156166(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014


MATHEMATICA

Select[Range[10^3], PrimeQ[(10^(# + 2) + 666)*10^# + 1] &] (* Arkadiusz Wesolowski, Sep 08 2011 *)


PROG

(PARI) for( n=1, 9999, ispseudoprime((10^(n+2)+666)*10^n+1) & print1(n", "))
(MAGMA) [n: n in [1..500]  IsPrime((10^(n+2)+666)*10^n+1)]; // Vincenzo Librandi, Nov 15 2014


CROSSREFS

Cf. A082700 and search results for 16661.
Cf. A232448 (a(n)  1).
Sequence in context: A302665 A041380 A151990 * A064125 A089031 A265152
Adjacent sequences: A156163 A156164 A156165 * A156167 A156168 A156169


KEYWORD

more,nonn,base


AUTHOR

M. F. Hasler, Feb 10 2009


EXTENSIONS

a(8) = 28292 (discovered on Jan 05 2004, by Daniel Heuer), Arkadiusz Wesolowski, Mar 16 2011
a(9) = 181299 from Serge Batalov, Nov 15 2014


STATUS

approved



