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A309201 a(n) is the smallest divisor of the Motzkin number A001006(n) not already in the sequence. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A253792 A058330 A124256

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

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Last modified May 20 12:55 EDT 2022. Contains 353871 sequences. (Running on oeis4.)