This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A244314 #23 Feb 26 2025 01:52:55 %S A244314 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 A244314 53,54,55,56,57,58,59,60,61,62,63,132,133,134,135,136,137,138,139,140, %U A244314 141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157 %N A244314 Nonnegative integers m such that the Semigreedy Catalan representation A244159(m) contains at least one zero. %C A244314 Starting offset is zero because A244159(0) = 0 is a borderline case (either one zero, or no zeros if leading zeros are discarded). %C A244314 From a(1)=2 onward the positions of zeros in A244233. %C A244314 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 A244314 Antti Karttunen, <a href="/A244314/b244314.txt">Table of n, a(n) for n = 0..9891</a> %F A244314 a(0) = 0, a(1) = 2, and for n >= 2, a(n) = n + A000108(1+A244317(n)) - A014143(A244317(n)-2) - 1. %o A244314 (Scheme) (define (A244314 n) (cond ((zero? n) 0) ((= 1 n) 2) (else (+ -1 n (- (A000108 (+ 1 (A244317 n))) (A014143 (- (A244317 n) 2))))))) %Y A244314 Subsequence of A244217. %Y A244314 Cf. A000108, A014138, A014143, A244233, A244159, A244217, A244317, A081291, A081293. %K A244314 nonn %O A244314 0,2 %A A244314 _Antti Karttunen_, Jun 25 2014