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 A090771 Numbers that are congruent to {1, 9} mod 10. 22
 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69, 71, 79, 81, 89, 91, 99, 101, 109, 111, 119, 121, 129, 131, 139, 141, 149, 151, 159, 161, 169, 171, 179, 181, 189, 191, 199, 201, 209, 211, 219, 221, 229, 231, 239, 241, 249, 251, 259, 261, 269, 271, 279, 281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Cf. property described by Gary Detlefs in A113801: more generally, these numbers are of the form (2*h*n + (h-4)*(-1)^n - h)/4 (h, n natural numbers), therefore ((2*h*n + (h-4)*(-1)^n - h)/4)^2-1 == 0 (mod h); in this case, a(n)^2 - 1 == 0 (mod 10). - Bruno Berselli, Nov 17 2010 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = (40* A057569(n) + 1)^(1/2). - Gary Detlefs, Feb 22 2010 From Bruno Berselli, Sep 16 2010 - Nov 17 2010: (Start)   G.f.: x*(1 + 8*x + x^2)/((1 + x)*(1 - x)^2).   a(n) = (10*n + 3*(-1)^n - 5)/2.   a(n) = -a(-n + 1) = a(n-1) + a(n-2) - a(n-3) = a(n-2) + 10.   a(n) = 10*A000217(n-1) + 1 - 2*sum(a(i), i = 1..n - 1) for n > 1. (End) a(n) = 10*n - a(n-1) - 10 (with a(1) = 1). - Vincenzo Librandi, Nov 16 2010 a(n) = sqrt(10*A132356(n-1) + 1). - Ivan N. Ianakiev, Nov 09 2012 MATHEMATICA Flatten[Table[10n - {9, 1}, {n, 30}]] (* Alonso del Arte, Sep 02 2014 *) PROG (Haskell) a090771 n = a090771_list !! (n-1) a090771_list = 1 : 9 : map (+ 10) a090771_list -- Reinhard Zumkeller, Jan 07 2012 (PARI) a(n)=n\2*10-(-1)^n \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A090298, A005408, A047209, A007310, A047336, A047522, A091998, A175886, A175887. Cf. A056020 (n = 1 or 8 mod 9), A175885 (n = 1 or 10 mod 11). Cf. A045468 (primes), A195142 (partial sums). Sequence in context: A182391 A263722 A299971 * A329279 A284295 A284294 Adjacent sequences:  A090768 A090769 A090770 * A090772 A090773 A090774 KEYWORD nonn,easy AUTHOR Giovanni Teofilatto, Feb 07 2004 EXTENSIONS Edited and extended by Ray Chandler, Feb 10 2004 STATUS approved

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Last modified March 30 21:56 EDT 2020. Contains 333132 sequences. (Running on oeis4.)