

A213257


a(1) = 1, a(2) = 2 and, for n > 2, a(n) is the smallest integer greater than a(n  1) such that no three terms of the sequence form a geometric progression of the form {x, 2 x, 4 x}.


2



1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 102, 103, 104, 105
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OFFSET

1,2


COMMENTS

Conjecture. The positive integers that are not in this sequence are given by the positions of 2 in the fixedpoint of the morphism 0>01, 1>02, 2>03, 3>01 (see A191255). (This has been confirmed for over 5000 terms of A213257.) To illustrate, the fixedpoint of the indicated morphism is {0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,1,0,1,0,2,0,...} and 2 occurs at positions {4,12,20,...}, integers that are missing in A213257.
The positive integers that are not in this sequence are listed in A213258.
For the sequence containing no 3term arithmetic progression,see A003278.


LINKS

Table of n, a(n) for n=1..90.


EXAMPLE

Given that the sequence begins {1, 2, 3, 5, 6, 7, 8, 9, 10, 11,...}, the next term, a(11), cannot be 12, because then the forbidden progression {3,6,12} would occur in the sequence. 13 is allowed, however, so a(11)=13.


CROSSREFS

Cf. A003278, A191255, A213258.
Sequence in context: A171521 A092784 A047588 * A039213 A326947 A256450
Adjacent sequences: A213254 A213255 A213256 * A213258 A213259 A213260


KEYWORD

nonn


AUTHOR

John W. Layman, Jun 07 2012


STATUS

approved



