A365424 - OEIS

%I #19 Sep 17 2023 12:10:21

%S 1,2,3,5,2,2,2,2,3,7,7,5,5,5,2,5,2,2,5,2,2,5,2,2,2,2,3,11,11,7,11,11,

%T 7,7,7,5,7,7,5,7,7,5,5,5,2,7,7,5,5,5,2,5,2,2,7,5,5,5,2,2,5,2,2,7,5,5,

%U 5,2,2,5,2,2,5,2,2,5,2,2,2,2,3,13,13,11,13,13,11,13,13,7,13,11,11,13,11,11,11,11,7

%N a(1) = 1, a(3^k) = 3 for k >= 1, and for any other n, a(n) is the last prime that is selected when the value of A356867(n) is computed with a greedy algorithm.

%C Apparently the analogous sequence for Doudna variant D(2) (A005940) is 1 followed by A000040(A290251(n-1)) for n >= 2: 1, 2, 3, 2, 5, 3, 3, 2, 7, 5, 5, 3, 5, 3, 3, 2, 11, 7, 7, 5, 7, etc.

%H Antti Karttunen, <a href="/A365424/b365424.txt">Table of n, a(n) for n = 1..59049</a>

%F a(1) = 1, and for n > 1, if n is of the form 3^k, then a(n) = 3, otherwise a(n) = A356867(n) / A356867(A365459(n)).

%o (PARI)

%o up_to = (3^10);

%o A365424list(up_to) = { my(v=vector(up_to),pv=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==sumdigits(i,3), v[i] = i; pv[i] = if(1==i,i,3); h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; pv[i] = p; break))); mapput(met,v[i],i)); (pv); };

%o v365424 = A365424list(up_to);

%o A365424(n) = v365424[n];

%Y Cf. A000040, A000244 (positions of the initial 1 and all 3's), A053735, A356867, A365459.

%Y Cf. also A005940, A290251.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 17 2023