The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A274213 Meta recurrence: a(0) = 1, a(1) = 2, a(2) = 3, a(n) = a(n - a(n-3)) + 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 (list; graph; refs; listen; history; text; internal format)
 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 t-2 times. In general, the meta recurrence a(n) = a(n-a(n-k))+k with initial conditions a(i) = i+1 for i = 0,...,k-1 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 t-k+1 times. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 PROG (Python) A274213_list = [1, 2, 3] for n in range(3, 10001): A274213_list.append(A274213_list[-A274213_list[-3]]+3) (Magma) I:=[1, 2, 3]; [n le 3 select I[n] else Self(n-Self(n-3))+3 : n in [1..80]]; // Vincenzo Librandi, Jun 18 2016 CROSSREFS Cf. A193358 Sequence in context: A085273 A151850 A290223 * A350315 A078706 A077082 Adjacent sequences: A274210 A274211 A274212 * A274214 A274215 A274216 KEYWORD nonn AUTHOR Chai Wah Wu, Jun 13 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 2 21:56 EST 2024. Contains 370498 sequences. (Running on oeis4.)