A244216 Numbers n that are at least twice the size the largest Catalan number less than or equal to n.

4, 10, 11, 12, 13, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 264

Offset

1,1

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 (cf. A014418) starts with digit 2 or 3.

Links

Antti Karttunen, Table of n, a(n) for n = 1..9878

Example

4 is present, as the largest Catalan number (A000108(k), here C(k)) less than or equal to 4 is C(2) = 2, and 4 >= 2*2.
5 is not present, as the largest Catalan number <= 5 is C(3) = 5, and 5 < 2*5.
10 is present, as the largest Catalan number <= 10 is C(3) = 5, and 10 >= 2*5.
11 is present, as the largest Catalan number <= 11 is C(3) = 5, and 11 >= 2*5.
27 is not present, as the largest Catalan number <= 27 is C(4) = 14, and 27 < 2*14.
28 is present, as the largest Catalan number <= 28 is C(4) = 14, and 28 >= 2*14.

Prog

(Scheme, with Antti Karttunen's IntSeq-library, two alternative definitions)
(define A244216 (MATCHING-POS 1 1 (lambda (k) (>= k (* 2 (A081290 k))))))
(define A244216 (ZERO-POS 0 0 A244215))

Crossrefs

Positions of zeros in A244215. Complement of A244217.

Cf. A000108, A014418, A081290.

Sequence in context: A292954 A355497 A045855 * A240580 A102535 A074226

Adjacent sequences: A244213 A244214 A244215 * A244217 A244218 A244219

Keyword

nonn

Author

Antti Karttunen, Jun 23 2014

Status

approved