A232449 The palindromic Belphegor numbers: (10^(n+3)+666)*10^(n+1)+1.

16661, 1066601, 100666001, 10006660001, 1000066600001, 100000666000001, 10000006660000001, 1000000066600000001, 100000000666000000001, 10000000006660000000001, 1000000000066600000000001, 100000000000666000000000001, 10000000000006660000000000001, 1000000000000066600000000000001

Offset

0,1

Comments

Though this sequence rarely contains primes (see A232448), most of its members tend to contain a few very large prime factors. The name stems from 'Belphegor's Prime', a(13), which was so named by Clifford Pickover (see link). [Comment corrected by N. J. A. Sloane, Dec 14 2015]

Links

Stanislav Sykora, Table of n, a(n) for n = 0..497

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 Number

Wikipedia, Belphegor's prime

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

a(n) = 666*10^(n+1)+100^(n+2)+1.

G.f.: (16661 - 782770*x + 767000*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)). [Bruno Berselli, Nov 25 2013]

Prog

(PARI) Belphegor(k)=(10^(k+3)+666)*10^(k+1)+1; nmax = 498; v = vector(nmax); for (n=0, #v-1, v[n+1]=Belphegor(n))

Crossrefs

Cf. A232448, A232450, A232451.

Subsequence of A118598.

Sequence in context: A317179 A196023 A108843 * A260312 A345573 A345829

Adjacent sequences: A232446 A232447 A232448 * A232450 A232451 A232452

Keyword

nonn,easy

Author

Stanislav Sykora, Nov 24 2013

Status

approved