A364958 Fixed points of A356867, where A356867 is Sycamore's Doudna variant D(3).

1, 2, 3, 6, 8, 9, 18, 24, 27, 54, 72, 81, 91, 162, 216, 243, 273, 486, 648, 729, 819, 1458, 1944, 2187, 2457, 4374, 5832, 6561, 7371, 13122, 17496, 19683, 22113, 39366, 52488, 59049, 66339, 118098, 157464, 177147, 199017, 354294, 472392, 531441, 597051, 1062882, 1417176, 1594323, 1791153, 3188646, 4251528, 4782969

Offset: 1

Author

David James Sycamore and Antti Karttunen, Sep 15 2023

Keywords

• nonn

Comments

Conjecture: All terms are of the form k*3^n, where k = 1,2,8,91, and n >= 0. - David James Sycamore, Aug 16 2023

Crossrefs

Fixed points of A356867 and of A365390, positions of 0's in A365462.

Programs

Mathematica

Block[{a, c, i, j, k, m, p, t, nn},
  nn = 3^12; m = 1; i = 2; p = Prime[i]; c[_] = False;
  Monitor[Reap[Do[Set[{m, k}, {1, n - p^Floor[Log[p, n]]}];
    If[k == 0, Sow[n]; Set[{a[n], c[n]}, {n, True}],
      While[Set[t, Prime[m] a[k]]; Or[m == i, c[t]], m++];
      If[t == n, Sow[n]]; Set[{a[n], c[t]}, {t, True}] ],
{n, nn}] ][[-1, 1]], n] ] (* Michael De Vlieger, Jul 02 2025 *)

PARI

up_to = 3^14;
A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==vecsum(digits(i,3)), v[i] = i; h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; break))); mapput(met,v[i],i)); (v); };
v356867 = A356867list(up_to);
A356867(n) = v356867[n];
isA364958(n) = (A356867(n)==n);

Formula

{k | k==A356867(k)}.