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 A017173 a(n) = 9n + 1. 29
 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 199, 208, 217, 226, 235, 244, 253, 262, 271, 280, 289, 298, 307, 316, 325, 334, 343, 352, 361, 370, 379, 388, 397, 406, 415, 424, 433, 442, 451, 460, 469, 478 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also all the numbers with digital root 1; A010888(a(n)) = 1. - Rick L. Shepherd, Jan 12 2009 A116371(a(n)) = A156144(a(n)); positions where records occur in A156144: A156145(n+1) = A156144(a(n)). - Reinhard Zumkeller, Feb 05 2009 If A=[A147296] 9*n^2+2*n (n>0, 11, 40, 87, ...); Y=[A010701] 3 (3, 3, 3, ...,); X=[A017173] 9*n+1 (n>0, 10, 19, 28, ...), we have, for all terms, Pell's equation X^2 - A*Y^2 = 1. Example: 10^2 - 11*3^2 = 1; 19^2 - 40*3^2 = 1; 28^2 - 87*3^2 = 1. - Vincenzo Librandi, Aug 01 2010 LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA G.f.: (1+8*x)/(1-x)^2. a(n) = 2*a(n-1) - a(n-2) with a(0)=1, a(1)=10. - Vincenzo Librandi, Aug 01 2010 EXAMPLE For n=2, a(2) = 2*10 - 1 = 19; n=3, a(3) = 2*19 - 10 = 28; n=4, a(4) = 2*28 - 19 = 37. - Vincenzo Librandi, Aug 01 2010 MATHEMATICA Range[1, 1000, 9] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *) LinearRecurrence[{2, -1}, {1, 10}, 60] (* Harvey P. Dale, Dec 27 2014 *) PROG (Sage) [i+1 for i in range(480) if gcd(i, 9) == 9] # Zerinvary Lajos, May 20 2009 (PARI) forstep(n=1, 500, 9, print1(n", ")) \\ Charles R Greathouse IV, May 28 2011 (Haskell) a017173 = (+ 1) . (* 9) a017173_list = [1, 10 ..]  -- Reinhard Zumkeller, Feb 04 2014 CROSSREFS Cf. A093644 ((9, 1) Pascal, column m=1). Cf. A010888. - Rick L. Shepherd, Jan 12 2009 Cf. A147296, A010701. - Vincenzo Librandi, Mar 11 2009 Sequence in context: A098750 A089756 A097153 * A276871 A247465 A088410 Adjacent sequences:  A017170 A017171 A017172 * A017174 A017175 A017176 KEYWORD nonn,easy AUTHOR STATUS approved

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