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A332116
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a(n) = (10^(2n+1)-1)/9 + 5*10^n.
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5
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6, 161, 11611, 1116111, 111161111, 11111611111, 1111116111111, 111111161111111, 11111111611111111, 1111111116111111111, 111111111161111111111, 11111111111611111111111, 1111111111116111111111111, 111111111111161111111111111, 11111111111111611111111111111, 1111111111111116111111111111111
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OFFSET
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0,1
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COMMENTS
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See A107126 = {10, 14, 40, 59, 160, 412, ...} 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)6(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11611...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) + 6*10^n = A002275(2n+1) + 5*10^n.
G.f.: (6 - 505*x + 400*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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A332116 := n -> (10^(2*n+1)-1)/9+5*10^n;
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MATHEMATICA
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Array[(10^(2 # + 1)-1)/9 + 5*10^# &, 15, 0]
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PROG
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(PARI) apply( {A332116(n)=10^(n*2+1)\9+5*10^n}, [0..15])
(Python) def A332116(n): return 10**(n*2+1)//9+5*10**n
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CROSSREFS
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Cf. (A077706-1)/2 = A107126: 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. A332126 .. A332196 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
Sequence in context: A120277 A241453 A193370 * A015086 A052466 A280477
Adjacent sequences: A332113 A332114 A332115 * A332117 A332118 A332119
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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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