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A232448 Belphegor primes: numbers n such that A232449(n) is prime. 4
0, 13, 42, 506, 608, 2472, 2623, 28291, 181298 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The resulting primes might be called Belphegor primes, after Pickover (see link). - N. J. A. Sloane, Dec 14 2015

LINKS

Table of n, a(n) for n=0..8.

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.

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: A242544 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(8) based on A156166 from Eric W. Weisstein, Jan 24 2017

STATUS

approved

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Last modified June 26 02:24 EDT 2017. Contains 288749 sequences.