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 A255582 a(n)=n when n <= 3, otherwise a(n) is the smallest positive number not yet in the sequence such that gcd(a(n), a(n-1)) <= gcd(a(n), a(n-2)) > 1. 18
 1, 2, 3, 4, 6, 8, 9, 10, 12, 5, 14, 15, 7, 18, 21, 16, 27, 20, 33, 24, 11, 26, 22, 13, 28, 39, 32, 30, 34, 25, 17, 35, 51, 40, 42, 38, 36, 19, 44, 57, 46, 45, 23, 48, 69, 50, 54, 52, 58, 56, 29, 49, 87, 63, 60, 77, 62, 55, 31, 65, 93, 70, 66, 64, 74, 68, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is a permutation of the natural numbers: the proof for A098550 applies with essentially no changes. [Confirmed by N. J. A. Sloane, Feb 27 2015] For n > 3, all primes first appear in order as composites with one smaller prime (proof similar to that in A098550). For any given set S of primes, the subsequence consisting of numbers whose prime factors are exactly the primes in S appears in increasing order. For example, if S = {2,3}, 6 appears first, followed by 12, 18, 24, 36, 48, 54, 72, etc. Appears to be very similar to A064413. Compare the respective inverses A255479 and A064664; see also A255482. Speaking very loosely, the ratio a(n)/n seems to be about 1/2, 1, or 3/2, just as for A064413, although this is a long way from being proved for either sequence. David Applegate points out that this is (presumably) because primes p >= 13 always occur as part of a subsequence 2p X p Y 3p, and subsequences 2p X p Y 5p, 2p X p Y 7p, etc. that produced the extra curves in the graph of A098550 just do not happen. - N. J. A. Sloane, Feb 27 2015, Mar 05 2015. First differs from A254077 at a(29). - Omar E. Pol, May 21 2015 LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..10000 David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015. MATHEMATICA a[n_] := a[n] = If[n<5, n, For[k=5, True, k++, If[FreeQ[Array[a, n-1], k], If[GCD[k, a[n-2]]>1 && GCD[k, a[n-1]] <= GCD[k, a[n-2]], Return[k]]]]]; Array[a, 100] (* Jean-François Alcover, Jul 31 2018 *) PROG (Haskell) import Data.List (delete) a255582 n = a255582_list !! (n-1) a255582_list = 1 : 2 : 3 : f 2 3 [4..] where f u v ws = y : f v y (delete y ws) where y = head [z | z <- ws, let d = gcd u z, d > 1, gcd v z <= d] -- Reinhard Zumkeller, Mar 10 2015 CROSSREFS Cf. A098550, A254077, A064413, A064664, A255480, A255481, A255482, A256974. A255479 is the inverse permutation. A256424 is a smoothed version. A256529 gives the partial sums. Sequence in context: A047302 A121217 A357992 * A254077 A352968 A156657 Adjacent sequences: A255579 A255580 A255581 * A255583 A255584 A255585 KEYWORD nonn,hear AUTHOR Bob Selcoe, Feb 26 2015 EXTENSIONS a(41)-a(67) from Hiroaki Yamanouchi, Feb 27 2015 STATUS approved

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Last modified November 29 13:49 EST 2023. Contains 367445 sequences. (Running on oeis4.)