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A056020
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Numbers that are congruent to +-1 mod 9.
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27
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1, 8, 10, 17, 19, 26, 28, 35, 37, 44, 46, 53, 55, 62, 64, 71, 73, 80, 82, 89, 91, 98, 100, 107, 109, 116, 118, 125, 127, 134, 136, 143, 145, 152, 154, 161, 163, 170, 172, 179, 181, 188, 190, 197, 199, 206, 208, 215, 217, 224, 226, 233, 235, 242, 244, 251, 253
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OFFSET
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1,2
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COMMENTS
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Or, numbers k such that k^2 == 1 (mod 9).
Or, numbers k such that the iterative cycle j -> sum of digits of j^2 when started at k contains a 1. E.g., 8 -> 6+4 = 10 -> 1+0+0 = 1 and 17 -> 2+8+9 = 19 -> 3+6+1 = 10 -> 1+0+0 = 1. - Asher Auel (asher.auel(AT)reed.edu), May 17 2001
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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a(1) = 1; a(n) = 9(n-1) - a(n-1). - Rolf Pleisch, Jan 31 2008 [Offset corrected by Jon E. Schoenfield, Dec 22 2008]
From R. J. Mathar, Feb 10 2008: (Start)
O.g.f.: 1 + 5/(4(x+1)) + 27/(4(-1+x)) + 9/(2(-1+x)^2).
a(n+1) - a(n) = A010697(n). (End)
a(n) = (9*A132355(n) + 1)^(1/2). - Gary Detlefs, Feb 22 2010
a(n) = (1/4)*(-9 + 5*(-1)^n + 18*n). - Paolo P. Lava, Apr 26 2010
From Bruno Berselli, Nov 17 2010: (Start)
a(n) = a(n-2) + 9, for n > 2.
a(n) = 9*A000217(n-1) + 1 - 2*Sum_{i=1..n-1} a(i), n > 1. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi/9)*cot(Pi/9) = A019676 * A019968. - Amiram Eldar, Dec 04 2021
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MATHEMATICA
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Select[ Range[ 300 ], PowerMod[ #, 2, 3^2 ]==1& ]
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PROG
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(PARI) a(n)=9*(n>>1)+if(n%2, 1, -1) \\ Charles R Greathouse IV, Jun 29 2011
(PARI) for(n=1, 40, print1(9*n-8, ", ", 9*n-1, ", ")) \\ Charles R Greathouse IV, Jun 29 2011
(Haskell)
a056020 n = a056020_list !! (n-1)
a05602_list = 1 : 8 : map (+ 9) a056020_list
-- Reinhard Zumkeller, Jan 07 2012
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CROSSREFS
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Cf. A007953, A047522 (n=1 or 7 mod 8), A090771 (n=1 or 9 mod 10).
Cf. A129805 (primes), A195042 (partial sums).
Cf. A005408, A019676, A019968, A047209, A007310, A047336, A175885, A091998, A175886, A113801, A175887.
Sequence in context: A038209 A319293 A061908 * A049510 A121846 A059094
Adjacent sequences: A056017 A056018 A056019 * A056021 A056022 A056023
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KEYWORD
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nonn,easy
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AUTHOR
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Robert G. Wilson v, Jun 08 2000
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STATUS
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approved
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