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A332119
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a(n) = (10^(2n+1)-1)/9 + 8*10^n.
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13
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9, 191, 11911, 1119111, 111191111, 11111911111, 1111119111111, 111111191111111, 11111111911111111, 1111111119111111111, 111111111191111111111, 11111111111911111111111, 1111111111119111111111111, 111111111111191111111111111, 11111111111111911111111111111, 1111111111111119111111111111111
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OFFSET
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0,1
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COMMENTS
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See A107649 = {1, 4, 26, 187, 226, 874, ...} for the indices of primes.
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LINKS
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Table of n, a(n) for n=0..15.
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
Patrick De Geest, Palindromic Wing Primes: (1)9(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11911...11, updated Dec 11 2018.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
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FORMULA
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a(n) = A138148(n) + 9*10^n = A002275(2n+1) + 8*10^n.
G.f.: (9 - 808*x + 700*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
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MAPLE
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A332119 := n -> (10^(2*n+1)-1)/9+8*10^n;
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MATHEMATICA
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Array[(10^(2 # + 1)-1)/9 + 8*10^# &, 15, 0]
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PROG
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(PARI) apply( {A332119(n)=10^(n*2+1)\9+8*10^n}, [0..15])
(Python) def A332119(n): return 10**(n*2+1)//9+8*10**n
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CROSSREFS
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Cf. (A077795-1)/2 = A107649: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332129 .. A332189 (variants with different repeated digit 2, ..., 8).
Cf. A332112 .. A332118 (variants with different middle digit 2, ..., 8).
Sequence in context: A119291 A113269 A307387 * A261826 A184688 A189178
Adjacent sequences: A332116 A332117 A332118 * A332120 A332121 A332122
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KEYWORD
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nonn,base,easy
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AUTHOR
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M. F. Hasler, Feb 09 2020
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STATUS
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approved
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