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 A120685 Integers m such that the sequence defined by f(0)=m and f(n+1)=1+gpf(f(n)), with gpf(n) being the greatest prime factor of n (A006530), ends up in the repetitive cycle 4 -> 3 -> 3 -> ... 5
 2, 4, 5, 8, 10, 11, 13, 15, 16, 17, 20, 22, 23, 25, 26, 30, 32, 33, 34, 37, 39, 40, 41, 44, 45, 46, 47, 50, 51, 52, 53, 55, 60, 61, 64, 65, 66, 68, 69, 71, 74, 75, 77, 78, 80, 82, 83, 85, 88, 90, 91, 92, 94, 97, 99, 100, 102, 104, 106, 107, 110, 111, 113, 115, 117, 119, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let f(0)=m; f(n+1)=1+gpf(f(n)), where gpf(n) is the greatest prime factor of n (A006530). For any m, for sufficiently large n the sequence f(n) oscillates between 3 and 4. Given a sufficiently large n, this allows us to divide integers in two classes: C3 (m such that the sequence f(n) enters the cycle 3, 4, 3, ...) and C4 (m such that the sequence f(n) enters the cycle 4, 3, 4, ...). We present here C4 as the one that begin with 4. In A120684 we present C3 as the one that begin with 3. LINKS EXAMPLE Oscillation between 3 and 4: 1+gpf(3)=1+3=4; 1+gpf(4)=1+2=3. Other value, e.g. 7: 1+gpf(7)=1+7=8; 1+gpf(8)=1+2=3 (7 belongs to C3). Other value, e.g. 20: 1+gpf(20)=1+5=6; 1+gpf(6)=1+3=4 (20 belongs to C4). MATHEMATICA f = Function[n, FactorInteger[n][[ -1, 1]] + 1]; mn = Map[(NestList[f, #, 8][[ -1]]) &, Range[2, 500]]; out = Flatten[Position[mn, 4]] + 1 CROSSREFS Cf. A120684, A072268, A006530. Sequence in context: A026138 A026170 A026174 * A284472 A160545 A161790 Adjacent sequences:  A120682 A120683 A120684 * A120686 A120687 A120688 KEYWORD nonn AUTHOR Carlos Alves, Jun 25 2006 EXTENSIONS Edited by Michel Marcus, Feb 25 2013 STATUS approved

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Last modified October 18 03:25 EDT 2021. Contains 348065 sequences. (Running on oeis4.)