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 A001281 Image of n under the map n->n/2 if n even, n->3n-1 if n odd. 14
 0, 2, 1, 8, 2, 14, 3, 20, 4, 26, 5, 32, 6, 38, 7, 44, 8, 50, 9, 56, 10, 62, 11, 68, 12, 74, 13, 80, 14, 86, 15, 92, 16, 98, 17, 104, 18, 110, 19, 116, 20, 122, 21, 128, 22, 134, 23, 140, 24, 146, 25, 152, 26, 158, 27, 164, 28, 170, 29, 176, 30, 182, 31, 188 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS On the set of positive integers, the orbit of any number seems to end in the orbit of 1, of 5 or of 17. Writing n=1+q*2^p with q odd, it is easily seen that for p=0,1 and p>3, some iterations of the map lead to a strictly smaller number (for n>17). The cases p=2 and p=3 may give rise to bigger loops (depending on the form of q). See sequences A135727-A135729 for maxima of the orbits and corresponding record indices. - M. F. Hasler, Nov 29 2007 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, E16. LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23. Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1) FORMULA f(n) = (7n-2-(5n-2)*cos(pi n))/4. [Robert W. Craigen (craigen(AT)fresno.edu)] G.f.: x*(2 + x + 4*x^2)/((1 - x)^2*(1 + x)^2). - Ilya Gutkovskiy, Aug 17 2016 MAPLE f := n-> if n mod 2 = 0 then n/2 else 3*n-1; fi; MATHEMATICA Table[If[OddQ[n], 3*n-1, n/2], {n, 0, 100}] (* T. D. Noe, Jun 27 2012 *) PROG (PARI) A001281(n)=if(n%2, 3*n-1, n>>1) \\ M. F. Hasler, Nov 29 2007 CROSSREFS Cf. A037082. Cf. A037084, A039500-A039505, A135727-A135730. See also A006370, A006577 (Collatz 3x+1 problem). Sequence in context: A154175 A257777 A011208 * A331312 A232535 A065826 Adjacent sequences:  A001278 A001279 A001280 * A001282 A001283 A001284 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 22 16:50 EDT 2020. Contains 337291 sequences. (Running on oeis4.)