A244314 Nonnegative integers n such that Semigreedy Catalan representation A244159(n) contains at least one zero.

0, 2, 5, 6, 7, 14, 15, 16, 17, 18, 19, 20, 21, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157

Offset

0,2

Comments

Starting offset is zero because A244159(0) = 0 is a borderline case (either one zero, or no zeros if leading zeros are discarded).

From a(1)=2 onward the positions of zeros in A244233.

After zero consists of successive subsequences containing terms from A000108(k) to (A000108(k)+A014138(k-2)-1) computed from k >= 2 onward, as: [2], [5,6,7], [14 .. 21], [42 .. 63], [132 .. 195], [429 .. 624], [1430 .. 2054], [4862 .. 6916], etc.

Links

Antti Karttunen, Table of n, a(n) for n = 0..9891

Formula

a(0) = 0, a(1) = 2, and for n >= 2, a(n) = n + A000108(1+A244317(n)) - A014143(A244317(n)-2)) - 1.

Prog

(Scheme) (define (A244314 n) (cond ((zero? n) 0) ((= 1 n) 2) (else (+ -1 n (- (A000108 (+ 1 (A244317 n))) (A014143 (- (A244317 n) 2)))))))

Crossrefs

Subsequence of A244217.

Cf. A000108, A014138, A014143, A244233, A244159, A244217, A244317, A081291, A081293.

Sequence in context: A215761 A117548 A175135 * A014489 A286270 A346880

Adjacent sequences: A244311 A244312 A244313 * A244315 A244316 A244317

Keyword

nonn

Author

Antti Karttunen, Jun 25 2014

Status

approved