A244314 - OEIS

%I #18 Jul 18 2014 18:46:42

%S 0,2,5,6,7,14,15,16,17,18,19,20,21,42,43,44,45,46,47,48,49,50,51,52,

%T 53,54,55,56,57,58,59,60,61,62,63,132,133,134,135,136,137,138,139,140,

%U 141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157

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

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

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

%C 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.

%H Antti Karttunen, <a href="/A244314/b244314.txt">Table of n, a(n) for n = 0..9891</a>

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

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

%Y Subsequence of A244217.

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

%K nonn

%O 0,2

%A _Antti Karttunen_, Jun 25 2014