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 A056020 Numbers that are congruent to +-1 mod 9. 27
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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, May 17 2001 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA 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 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 E.g.f.: 1 + ((18*x - 9)*exp(x) + 5*exp(-x))/4. - David Lovler, Sep 04 2022 MATHEMATICA Select[ Range[ 300 ], PowerMod[ #, 2, 3^2 ]==1& ] PROG (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 CROSSREFS 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 KEYWORD nonn,easy,changed AUTHOR Robert G. Wilson v, Jun 08 2000 STATUS approved

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Last modified February 27 12:56 EST 2024. Contains 370375 sequences. (Running on oeis4.)