A309201 - OEIS

%I #19 Jul 27 2019 14:37:25

%S 1,2,4,3,7,17,127,19,5,547,13,15511,15,6,9,284489,57,1089397,12,73,11,

%T 21,35,63,119,6417454619,38,107,31,1483,497461,4644523115569,51,10,37,

%U 953467954114363,1601,370537,1063,1301337253214147,43,18,1951,520497658389713341

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

%C 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.

%C In fact _Daniel Suteu_ points out that Eu and Liu (2008) prove that no Motzkin number is a multiple of 8.

%C 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.

%H Daniel Suteu, <a href="/A309201/b309201.txt">Table of n, a(n) for n = 1..191</a>

%H Eu, Sen-Peng & Liu, Shu-Chung & Yeh, Yeong-nan, <a href="https://www.math.sinica.edu.tw/www/file_upload/mayeh/2008CatalanandMotzkinnumbersmodulo4and8.pdf">Catalan and Motzkin numbers modulo 4 and 8</a>, EJC (2008).

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jul 25 2019

%E More terms from _Daniel Suteu_, Jul 25 2019