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 A225381 Elimination order of the first person in a Josephus problem. 2
 1, 2, 2, 4, 3, 5, 4, 8, 5, 8, 6, 11, 7, 11, 8, 16, 9, 14, 10, 18, 11, 17, 12, 23, 13, 20, 14, 25, 15, 23, 16, 32, 17, 26, 18, 32, 19, 29, 20, 38, 21, 32, 22, 39, 23, 35, 24, 47, 25, 38, 26, 46, 27, 41, 28, 53, 29, 44, 30, 53, 31, 47, 32, 64, 33, 50, 34, 60, 35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In a Josephus problem such as A006257, a(n) is the order in which the person originally first in line is eliminated. The number of remaining survivors after the person originally first in line has been eliminated, i.e., n-a(n), gives the fractal sequence A025480. For the linear version, see A225489. LINKS FORMULA a(n) = (n+1)/2 (odd n); a(n) = a(n/2) + n/2 (even n). a(n) = n - A025480(n). G.f.: Sum{n>=1} x^n/(1-x^A006519(n)). - Nicolas Nagel, Mar 19 2018 EXAMPLE If there are 7 persons to begin with, they are eliminated in the following order: 2,4,6,1,5,3,7. So the first person (the person originally first in line) is eliminated as number 4. Therefore a(7) = 4. MATHEMATICA t = {1}; Do[AppendTo[t, If[OddQ[n], (n + 1)/2, t[[n/2]] + n/2]], {n, 2, 100}]; t (* T. D. Noe, May 17 2013 *) CROSSREFS Cf. A006257, A025480, A225489. Sequence in context: A204900 A070803 A071693 * A007728 A262991 A077026 Adjacent sequences:  A225378 A225379 A225380 * A225382 A225383 A225384 KEYWORD nonn AUTHOR Marcus Hedbring, May 17 2013 STATUS approved

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Last modified April 15 01:01 EDT 2021. Contains 342971 sequences. (Running on oeis4.)