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A232449
The palindromic Belphegor numbers: (10^(n+3)+666)*10^(n+1)+1.
4
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
Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)
Simon Singh, Homer Simpson's scary math problems. BBC News. Retrieved 31 October 2013.
Eric Weisstein's World of Mathematics, Belphegor Number
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
Subsequence of A118598.
Sequence in context: A317179 A196023 A108843 * A260312 A345573 A345829
KEYWORD
nonn,easy
AUTHOR
Stanislav Sykora, Nov 24 2013
STATUS
approved