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 A232448 Indices of Belphegor primes: numbers k such that the decimal number 1 0...0(k 0's) 666 0...0(k 0's) 1 (i.e., A232449(k)) is prime. 6
 0, 13, 42, 506, 608, 2472, 2623, 28291, 181298 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The resulting primes might be called Belphegor primes, after Pickover (see link). - N. J. A. Sloane, Dec 14 2015 I suspect the larger numbers only correspond to probable primes. - N. J. A. Sloane, Oct 16 2018 The numbers correspond to proven primes for n <= 9. - Jens Kruse Andersen, Mar 25 2021 LINKS Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018) Clifford A. Pickover, Belphegor's Prime: 1000000000000066600000000000001 Simon Singh, Homer Simpson's scary math problems. BBC News. Retrieved 31 October 2013. Eric Weisstein's World of Mathematics, Belphegor Prime Eric Weisstein's World of Mathematics, Integer Sequence Primes Wikipedia, Belphegor's prime FORMULA a(n) = A156166(n) - 1. EXAMPLE 0 is in the sequence because A232449(0) = 16661 is prime. 13 is in the sequence because A232449(13) = 1000000000000066600000000000001 is prime. For k = 1..12, A232449(k) is composite. 42 is in the sequence because 10000000000000000000000000000000000000000006660000000000000000000000000000\ 000000000000001 is a (probable) prime. - N. J. A. Sloane, Oct 16 2018 MATHEMATICA lst = {}; Do[p = 10^(2*n + 4) + 666*10^(n + 1) + 1; If[PrimeQ[p], Print[n]], {n, 0, 3000}]; (* Nathaniel Johnston, Nov 25 2013 *) PROG (PARI) default(factor_proven, 1); Belphegor(k)=(10^(k+3)+666)*10^(k+1)+1; for (an=0, 10000,   if (isprime(Belphegor(an)), print("Found: ", an),       if (an%100==0, print("Tested up to: ", an))) ); CROSSREFS Cf. A232449 (Belphegor numbers), A232450, A232451. Cf. A156166 (= a(n) + 1). Sequence in context: A301539 A240517 A074022 * A157835 A071632 A259427 Adjacent sequences:  A232445 A232446 A232447 * A232449 A232450 A232451 KEYWORD nonn,more,hard AUTHOR Stanislav Sykora, Nov 24 2013 EXTENSIONS a(9) based on A156166 from Eric W. Weisstein, Jan 24 2017 Offset changed to 1 by Jon E. Schoenfield, Mar 23 2021 STATUS approved

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Last modified June 22 11:29 EDT 2021. Contains 345375 sequences. (Running on oeis4.)