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

1,2

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

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)).

Prog

(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];

Crossrefs

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

Cf. also A005940, A290251.

Sequence in context: A269701 A011157 A205387 * A060441 A255913 A065996

Adjacent sequences: A365421 A365422 A365423 * A365425 A365426 A365427

Keyword

nonn

Author

Antti Karttunen, Sep 17 2023

Status

approved