A251141 -id:A251141 - 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 *)

A251140 Total number of prime factors of A098550(n).

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 2, 2, 1, 2, 2, 3, 2, 4, 1, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 2, 5, 1, 3, 2, 4, 2, 2, 2, 4, 2, 3, 2, 2, 3, 1, 3, 2, 3, 2, 4, 2, 3, 1, 5, 2, 3, 3, 2, 4, 4, 2, 2, 1, 1, 2, 2, 6, 3, 3, 2, 4, 2, 4, 2, 3, 2, 5, 3, 2, 3, 1, 3, 2, 3, 3, 5, 2, 2

Offset: 1

Reinhard Zumkeller, Nov 30 2014

nonn

a(n) = A001222(A098550(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A001222, A098548, A251141, A251138.

a251140 = a001222 . fromIntegral . a098550

A251139 Number of distinct prime factors of A098548(n).

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3

Offset: 1

Reinhard Zumkeller, Nov 30 2014

nonn

a(n) = A001221(A098548(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A001221, A098548, A251138, A251141.

a251139 = a001221 . fromIntegral . a098548

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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A251140 Total number of prime factors of A098550(n).

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A251139 Number of distinct prime factors of A098548(n).

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Haskell