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A232449 The palindromic Belphegor numbers: (10^(n+3)+666)*10^(n+1)+1. 4


%S 16661,1066601,100666001,10006660001,1000066600001,100000666000001,

%T 10000006660000001,1000000066600000001,100000000666000000001,

%U 10000000006660000000001,1000000000066600000000001,100000000000666000000000001,10000000000006660000000000001,1000000000000066600000000000001

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

%C 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]

%H Stanislav Sykora, <a href="/A232449/b232449.txt">Table of n, a(n) for n = 0..497</a>

%H Tony Padilla and Brady Haran, <a href="https://www.youtube.com/watch?v=zk_Q9y_LNzg">The Most Evil Number</a>, Numberphile video (2018)

%H Clifford A. Pickover, <a href="http://sprott.physics.wisc.edu/pickover/pc/1000000000000066600000000000001.html">Belphegor's Prime: 1000000000000066600000000000001</a>

%H Simon Singh, <a href="http://www.bbc.co.uk/news/magazine-24724635">Homer Simpson's scary math problems</a>. BBC News. Retrieved 31 October 2013.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BelphegorNumber.html">Belphegor Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Belphegor%27s_Prime">Belphegor's prime</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

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

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

%o (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))

%Y Cf. A232448, A232450, A232451.

%Y Subsequence of A118598.

%K nonn,easy

%O 0,1

%A _Stanislav Sykora_, Nov 24 2013

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Last modified May 12 04:27 EDT 2021. Contains 343810 sequences. (Running on oeis4.)