A251536 -id:A251536 - cp's OEIS frontend

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).

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

Offset: 1

Reinhard Zumkeller, Sep 14 2004

nonn

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)).

Reinhard Zumkeller, 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 [math.NT], 2015 and J. Int. Seq. 18 (2015) 15.6.7.
Reinhard Zumkeller, Table of n, a(n) for n = 1..100000

Cf. A098549, A098550.
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.

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

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

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 *)

A251535 Bisection A098548(2n+1).

Original entry on oeis.org

1, 3, 9, 21, 27, 33, 39, 51, 57, 63, 69, 81, 87, 93, 99, 111, 117, 123, 129, 141, 147, 153, 159, 171, 177, 183, 189, 201, 207, 213, 219, 237, 243, 249, 261, 267, 273, 279, 291, 297, 303, 309, 321, 327, 333, 339, 351, 357, 363

Offset: 0

N. J. A. Sloane, Dec 07 2014

nonn

For a given n>0, imagine a continuously-running wall clock that chimes once every a(n) minutes. Let m equal the number of distinct minute marks the minute hand would point to over the course of time at each chime. This sequence defines the values of a(n) for m=20. An example of this sequence is depicted in Battlestar Galactica Season 1 Episode 1 "33" (from 2004) with a(5)=33. - David Martin, Nov 26 2019

Reinhard Zumkeller, Table of n, a(n) for n = 0..100000

Cf. A098548, A251536.

a251535 n = a251535_list !! n
a251535_list = fst a098548_bisect
a098548_bisect = cleave a098548_list where
   cleave xs = (evens xs, odds xs) where
      evens [] = []; evens [x] = [x]; evens (x:_:xs) = x : evens xs
      odds [] = []; odds [x] = []; odds (_:x:xs) = x : odds xs
-- Reinhard Zumkeller, Dec 08 2014

cp's OEIS Frontend

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).

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