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A232449
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The palindromic Belphegor numbers: (10^(n+3)+666)*10^(n+1)+1.
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4
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16661, 1066601, 100666001, 10006660001, 1000066600001, 100000666000001, 10000006660000001, 1000000066600000001, 100000000666000000001, 10000000006660000000001, 1000000000066600000000001, 100000000000666000000000001, 10000000000006660000000000001, 1000000000000066600000000000001
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OFFSET
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0,1
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COMMENTS
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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]
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LINKS
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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).
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FORMULA
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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]
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PROG
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(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))
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CROSSREFS
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Cf. A232448, A232450, A232451.
Subsequence of A118598.
Sequence in context: A317179 A196023 A108843 * A260312 A224572 A186311
Adjacent sequences: A232446 A232447 A232448 * A232450 A232451 A232452
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KEYWORD
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nonn,easy
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AUTHOR
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Stanislav Sykora, Nov 24 2013
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STATUS
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approved
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