A251411 Numbers k such that A098550(k) = k.

1, 2, 3, 4, 12, 50, 86

Offset: 1

Author

N. J. A. Sloane, Dec 02 2014

Keywords

• nonn
• more

Comments

There is a strong conjecture that there are no further terms. See the discussion in the comments in A098550.

References

• L. Edson Jeffery, Posting to Sequence Fans Mailing List, Nov 30 2014.

Links

• Hans Havermann, Loops and unresolved chains for map n -> A098550(n) trajectories
• 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 and J. Int. Seq. 18 (2015) 15.6.7.

Crossrefs

Cf. A098550, A251412, A251556.

Programs

Mathematica

max = 100;
f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, max - 3];
Select[Transpose[{Range[max], A098550}], #[[1]] == #[[2]]&][[All, 1]] (* Jean-François Alcover, Sep 05 2018, after Robert G. Wilson v in A098550 *)

Python

from math import gcd
A251411_list, l1, l2, s, b = [1,2,3], 3, 2, 4, {}
for n in range(4,10**4):
    i = s
    while True:
        if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:
            l2, l1, b[i] = l1, i, 1
            while s in b:
                b.pop(s)
                s += 1
            if i == n:
                A251411_list.append(n)
            break
        i += 1 # Chai Wah Wu, Dec 03 2014