A251535 -id:A251535 - 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 *)

A251539 First differences of A251538.

Original entry on oeis.org

4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 2, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4

Offset: 1

N. J. A. Sloane, Dec 07 2014

nonn

I would very much like to have a formula or recurrence for this sequence.

Reinhard Zumkeller, Table of n, a(n) for n = 1..100000

Cf. A098548, A251535-A251538.

Cf. A251767 (duplicates removed), A251768 (run lengths).

a251539 n = a251539_list !! (n-1)
a251539_list = zipWith (-) (tail a251538_list) a251538_list
-- Reinhard Zumkeller, Dec 08 2014

max = 1000 (* = max term of A251538 *);
A098548 = {1, 2, 3};
For[n = 4, n <= 8 max, n++, If[GCD[n, A098548[[-1]]] == 1 && GCD[n, A098548[[-2]]] > 1, AppendTo[A098548, n]]];
A251538 = Select[Range[max], A098548[[2#+3]] > A098548[[2#+1]] + 6&];
Differences[A251538] (* Jean-François Alcover, Aug 01 2018 *)

A251536 A098548(2n)/2.

Original entry on oeis.org

1, 2, 5, 11, 14, 17, 20, 26, 29, 32, 35, 41, 44, 47, 50, 56, 59, 62, 65, 71, 74, 77, 80, 86, 89, 92, 95, 101, 104, 107, 110, 119, 122, 125, 131, 134, 137, 140, 146, 149, 152, 155, 161, 164, 167, 170, 176, 179, 182, 185, 191

Offset: 1

N. J. A. Sloane, Dec 07 2014

nonn

Equals (A251535(n)+1)/2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..100000

Cf. A098548, A251535.

a251536 n = a251536_list !! (n-1)
a251536_list = map (flip div 2) $ snd a098548_bisect
-- where a098548_bisect is defined in a251535.
-- 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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A251539 First differences of A251538.

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A251536 A098548(2n)/2.

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