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 A191106 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 3x are in a. 9
 1, 3, 7, 9, 19, 21, 25, 27, 55, 57, 61, 63, 73, 75, 79, 81, 163, 165, 169, 171, 181, 183, 187, 189, 217, 219, 223, 225, 235, 237, 241, 243, 487, 489, 493, 495, 505, 507, 511, 513, 541, 543, 547, 549, 559, 561, 565, 567, 649, 651, 655, 657, 667, 669, 673, 675, 703, 705, 709, 711, 721, 723, 727, 729, 1459, 1461, 1465, 1467, 1477 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Examples for various choices of i and k: A003278:  (i,k)=(-2,-1) A191106:  (i,k)=(-2,0) A191107:  (i,k)=(-2,1) A191108:  (i,k)=(-2,2) A153775:  (i,k)=(-1,0) A147991:  (i,k)=(-1,1) A191109:  (i,k)=(-1,2) A005836:  (i,k)=(0,1) A191110:  (i,k)=(0,2) A132140:  (i,k)=(1,2) For a=A191106, we have closure properties: the integers in (2+a)/3 comprise a; the integers in a/3 comprise a. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, 10 (2007) 1-13. FORMULA a(n) = 2*A005836(n) + 1. - Charles R Greathouse IV, Sep 06 2011 a(n) = A005823(n) + 1. - Vladimir Shevelev, Dec 17 2012 EXAMPLE 1 -> 3 -> 7,9 -> 19,21,25,27 -> ... MATHEMATICA h = 3; i = -2; j = 3; k = 0; f = 1; g = 9; a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191106; regarding g, see note at A190803 *) b = (a + 2)/3; c = a/3; r = Range[1, 900]; d = Intersection[b, r](* illustrates closure property *) e = Intersection[c, r](* illustrates closure property *) CROSSREFS Cf. A190803. Sequence in context: A230116 A031273 A140118 * A110674 A003528 A032913 Adjacent sequences:  A191103 A191104 A191105 * A191107 A191108 A191109 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 26 2011 STATUS approved

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Last modified July 17 21:51 EDT 2018. Contains 312725 sequences. (Running on oeis4.)