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

Author

N. J. A. Sloane, Jul 25 2019

Keywords

• nonn

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.

Extensions

More terms from Daniel Suteu, Jul 25 2019