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A156166
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Numbers k > 0 such that (10^(k+2) + 666)*10^k + 1 is prime.
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4
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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C. Caldwell, H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), p. 32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
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FORMULA
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a(n) = A232448(n) + 1.
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MAPLE
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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
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MATHEMATICA
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Select[Range[10^3], PrimeQ[(10^(# + 2) + 666)*10^# + 1] &] (* Arkadiusz Wesolowski, Sep 08 2011 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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more,nonn,base
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AUTHOR
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M. F. Hasler, Feb 10 2009
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EXTENSIONS
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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
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STATUS
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approved
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