A364958 - OEIS

%I #11 Sep 17 2023 12:10:05

%S 1,2,3,6,8,9,18,24,27,54,72,81,91,162,216,243,273,486,648,729,819,

%T 1458,1944,2187,2457,4374,5832,6561,7371,13122,17496,19683,22113,

%U 39366,52488,59049,66339,118098,157464,177147,199017,354294,472392,531441,597051,1062882,1417176,1594323,1791153,3188646,4251528,4782969

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

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

%o (PARI)

%o up_to = 3^14;

%o 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 v356867 = A356867list(up_to);

%o A356867(n) = v356867[n];

%o isA364958(n) = (A356867(n)==n);

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

%K nonn

%O 1,2

%A _David James Sycamore_ and _Antti Karttunen_, Sep 15 2023