

A244217


Numbers n less than twice the largest Catalan number that is less than or equal to n.


5



1, 2, 3, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 132, 133, 134
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OFFSET

1,2


COMMENTS

Equally: Numbers k such that if m is the largest Catalan number <= k [= A081290(k)], then k < 2*m.
Numbers k such that the Greedy Catalan Base representation of k (A014418(k)) starts with digit 1.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..6918


EXAMPLE

41 is not a member, because the largest Catalan number less than or equal to 41 is C(4) = 14, and 41 is not less than 2*14 = 28.
42 is a member, because the largest Catalan number less than or equal to 42 is C(5) = 42 itself, and 42 certainly is less than 2*42 = 84.
See also the examples given for the complement of this sequence: A244216.


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary, two alternative implementations)
(define A244217 (NONZEROPOS 1 1 A244215))
(define A244217 (MATCHINGPOS 1 1 (lambda (k) (= 1 (car (A014418raw k)))))) ;; A014418raw given in A014418.


CROSSREFS

Positions of nonzeros in A244215.
Complement of A244216.
Cf. A000108 (a subsequence), A014418, A081290, A244314.
Sequence in context: A182942 A069224 A117578 * A039122 A031975 A028729
Adjacent sequences: A244214 A244215 A244216 * A244218 A244219 A244220


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jun 23 2014


STATUS

approved



