

A274213


Meta recurrence: a(0) = 1, a(1) = 2, a(2) = 3, a(n) = a(n  a(n3)) + 3 for n > 2.


2



1, 2, 3, 6, 6, 6, 4, 5, 6, 9, 9, 9, 9, 9, 9, 7, 8, 9, 12, 12, 12, 12, 12, 12, 12, 12, 12, 10, 11, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 14, 15, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 16, 17, 18, 21, 21, 21, 21, 21, 21, 21
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OFFSET

0,2


COMMENTS

The sequence is constructed by starting with 3*m copies of 3*(m+1), followed by 3*m+1, 3*m+2, 3*m+3, as m varies from 0, 1, 2, ... It is straightforward to check that this construction satisfies the recurrence relation.
The construction shows that the sequence is well defined, every positive integer is in the sequence, and every integer not a proper multiple of 3 appears only once. If t is a multiple of 3, then t appears t2 times.
In general, the meta recurrence a(n) = a(na(nk))+k with initial conditions a(i) = i+1 for i = 0,...,k1 has a simple solution and can be constructed starting with k*m copies of k*(m+1), followed by k*m+1, k*m+2, ..., k*(m+1), as m varies from 0, 1, 2, ... This sequence is well defined, every positive integer is in the sequence, and every integer not a proper multiple of k appears once. If t is a multiple of k, then t appears tk+1 times.


LINKS



PROG

(Python)
for n in range(3, 10001):
(Magma) I:=[1, 2, 3]; [n le 3 select I[n] else Self(nSelf(n3))+3 : n in [1..80]]; // Vincenzo Librandi, Jun 18 2016


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



