A365424 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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 17 2023

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..59049

Crossrefs

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

Cf. also A005940, A290251.

Programs

PARI

up_to = (3^10);
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); };
v365424 = A365424list(up_to);
A365424(n) = v365424[n];

Formula

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)).