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

%I A244217 #18 Jun 26 2014 18:52:10
%S A244217 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,
%T A244217 45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
%U A244217 68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,132,133,134
%N A244217 Numbers n less than twice the largest Catalan number that is less than or equal to n.
%C A244217 Equally: Numbers k such that if m is the largest Catalan number <= k [= A081290(k)], then k < 2*m.
%C A244217 Numbers k such that the Greedy Catalan Base representation of k (A014418(k)) starts with digit 1.
%H A244217 Antti Karttunen, <a href="/A244217/b244217.txt">Table of n, a(n) for n = 1..6918</a>
%e A244217 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.
%e A244217 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.
%e A244217 See also the examples given for the complement of this sequence: A244216.
%o A244217 (Scheme, with _Antti Karttunen_'s IntSeq-library, two alternative implementations)
%o A244217 (define A244217 (NONZERO-POS 1 1 A244215))
%o A244217 (define A244217 (MATCHING-POS 1 1 (lambda (k) (= 1 (car (A014418raw k)))))) ;; A014418raw given in A014418.
%Y A244217 Positions of nonzeros in A244215.
%Y A244217 Complement of A244216.
%Y A244217 Cf. A000108 (a subsequence), A014418, A081290, A244314.
%K A244217 nonn
%O A244217 1,2
%A A244217 _Antti Karttunen_, Jun 23 2014