A244217 Numbers n less than twice the largest Catalan number that is less than or equal to n.

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

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 IntSeq-library, two alternative implementations)
(define A244217 (NONZERO-POS 1 1 A244215))
(define A244217 (MATCHING-POS 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: A349095 A069224 A117578 * A351224 A039122 A355547

Adjacent sequences: A244214 A244215 A244216 * A244218 A244219 A244220

Keyword

nonn

Author

Antti Karttunen, Jun 23 2014

Status

approved