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A098548 a(n) = n if n <= 3, otherwise the smallest number > a(n-1) having at least one common factor with a(n-2) but none with a(n-1). 21
1, 2, 3, 4, 9, 10, 21, 22, 27, 28, 33, 34, 39, 40, 51, 52, 57, 58, 63, 64, 69, 70, 81, 82, 87, 88, 93, 94, 99, 100, 111, 112, 117, 118, 123, 124, 129, 130, 141, 142, 147, 148, 153, 154, 159, 160, 171, 172, 177, 178, 183, 184, 189, 190, 201, 202, 207, 208, 213, 214 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The number a(n) is even if and only if n is even. If n>=1, then a(2n) = a(2n-1) + 1. If n>=2, then a(2n+1) - a(2n) >= 5. As a consequence, if n>=15, then a(n) > 3n. - Benoit Jubin, Dec 07 2014
A098549(n) = a(a(n)).
LINKS
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015 and J. Int. Seq. 18 (2015) 15.6.7.
MAPLE
x2 := 0: for n from 1 to 1000 do x := x2 + 1: while (n >= 4 and (gcd(x, x2) > 1 or gcd(x, x1) = 1)) do x := x + 1: end do; print (n, x); x1 := x2: x2 := x: end do: # David Applegate, Nov 26 2014
MATHEMATICA
a := {1, 2, 3}; For[n = 4, n <= 1000, n++, If[GCD[n, a[[-1]]] == 1 && GCD[n, a[[-2]]] > 1, AppendTo[a, n]]]; a (* L. Edson Jeffery, Dec 04 2014 *)
PROG
(Haskell)
a098548 n = a098548_list !! (n-1)
a098548_list = 1 : 2 : 3 : f 2 3 [4..] where
f u v (w:ws) = if gcd u w > 1 && gcd v w == 1
then w : f v w ws else f u v ws
-- Reinhard Zumkeller, Nov 21 2014
CROSSREFS
Cf. A158478 (smallest prime factor), A251104 (largest prime factor), A251139 (number of distinct prime factors), A251141 (total number of prime factors), A251046 (squarefree part), A251090 (squarefree kernel).
Cf. also A251535 and A251536 (bisections), A251537, A251538, A251539 (jumps), A251540.
Sequence in context: A174437 A127150 A256189 * A076963 A081871 A366913
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 14 2004
STATUS
approved

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Last modified February 21 03:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)