A309201 a(n) is the smallest divisor of the Motzkin number A001006(n) not already in the sequence.

1, 2, 4, 3, 7, 17, 127, 19, 5, 547, 13, 15511, 15, 6, 9, 284489, 57, 1089397, 12, 73, 11, 21, 35, 63, 119, 6417454619, 38, 107, 31, 1483, 497461, 4644523115569, 51, 10, 37, 953467954114363, 1601, 370537, 1063, 1301337253214147, 43, 18, 1951, 520497658389713341

Offset

1,2

Comments

Is this a permutation of the positive integers? Daniel Suteu's b-file suggests the answer is no, since powers of 2 >= 8 seem to be missing.

In fact Daniel Suteu points out that Eu and Liu (2008) prove that no Motzkin number is a multiple of 8.

Given any monotonically increasing sequence {b(n): n >= 1} of positive integers we can define a sequence {a(n): n >= 1} by setting a(n) to be smallest divisor of b(n) not already in the {a(n)} sequence. The triangular numbers A000217 produce A111273. A000027 is fixed under this transformation.

Links

Daniel Suteu, Table of n, a(n) for n = 1..191

Eu, Sen-Peng & Liu, Shu-Chung & Yeh, Yeong-nan, Catalan and Motzkin numbers modulo 4 and 8, EJC (2008).

Crossrefs

Cf. A000027, A000108, A000217, A111273, A309200.

Sequence in context: A294244 A333028 A296449 * A360145 A253792 A058330

Adjacent sequences: A309198 A309199 A309200 * A309202 A309203 A309204

Keyword

nonn

Author

N. J. A. Sloane, Jul 25 2019

Extensions

More terms from Daniel Suteu, Jul 25 2019

Status

approved