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

%I A364958 #14 Jul 02 2025 20:30:36
%S A364958 1,2,3,6,8,9,18,24,27,54,72,81,91,162,216,243,273,486,648,729,819,
%T A364958 1458,1944,2187,2457,4374,5832,6561,7371,13122,17496,19683,22113,
%U A364958 39366,52488,59049,66339,118098,157464,177147,199017,354294,472392,531441,597051,1062882,1417176,1594323,1791153,3188646,4251528,4782969
%N A364958 Fixed points of A356867, where A356867 is Sycamore's Doudna variant D(3).
%C A364958 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
%F A364958 {k | k==A356867(k)}.
%t A364958 Block[{a, c, i, j, k, m, p, t, nn},
%t A364958   nn = 3^12; m = 1; i = 2; p = Prime[i]; c[_] = False;
%t A364958   Monitor[Reap[Do[Set[{m, k}, {1, n - p^Floor[Log[p, n]]}];
%t A364958     If[k == 0, Sow[n]; Set[{a[n], c[n]}, {n, True}],
%t A364958       While[Set[t, Prime[m] a[k]]; Or[m == i, c[t]], m++];
%t A364958       If[t == n, Sow[n]]; Set[{a[n], c[t]}, {t, True}] ],
%t A364958 {n, nn}] ][[-1, 1]], n] ] (* _Michael De Vlieger_, Jul 02 2025 *)
%o A364958 (PARI)
%o A364958 up_to = 3^14;
%o A364958 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); };
%o A364958 v356867 = A356867list(up_to);
%o A364958 A356867(n) = v356867[n];
%o A364958 isA364958(n) = (A356867(n)==n);
%Y A364958 Fixed points of A356867 and of A365390, positions of 0's in A365462.
%K A364958 nonn
%O A364958 1,2
%A A364958 _David James Sycamore_ and _Antti Karttunen_, Sep 15 2023