cp's OEIS Frontend

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

%I A244216 #16 Jun 26 2014 18:51:10
%S A244216 4,10,11,12,13,28,29,30,31,32,33,34,35,36,37,38,39,40,41,84,85,86,87,
%T A244216 88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
%U A244216 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
%N A244216 Numbers n that are at least twice the size the largest Catalan number less than or equal to n.
%C A244216 Equally: Numbers k such that if m is the largest Catalan number <= k [= A081290(k)], then k >= 2*m.
%C A244216 Numbers k such that the Greedy Catalan Base representation of k (cf. A014418) starts with digit 2 or 3.
%H A244216 Antti Karttunen, <a href="/A244216/b244216.txt">Table of n, a(n) for n = 1..9878</a>
%e A244216 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.
%e A244216 5 is not present, as the largest Catalan number <= 5 is C(3) = 5, and 5 < 2*5.
%e A244216 10 is present, as the largest Catalan number <= 10 is C(3) = 5, and 10 >= 2*5.
%e A244216 11 is present, as the largest Catalan number <= 11 is C(3) = 5, and 11 >= 2*5.
%e A244216 27 is not present, as the largest Catalan number <= 27 is C(4) = 14, and 27 < 2*14.
%e A244216 28 is present, as the largest Catalan number <= 28 is C(4) = 14, and 28 >= 2*14.
%o A244216 (Scheme, with _Antti Karttunen_'s IntSeq-library, two alternative definitions)
%o A244216 (define A244216 (MATCHING-POS 1 1 (lambda (k) (>= k (* 2 (A081290 k))))))
%o A244216 (define A244216 (ZERO-POS 0 0 A244215))
%Y A244216 Positions of zeros in A244215. Complement of A244217.
%Y A244216 Cf. A000108, A014418, A081290.
%K A244216 nonn
%O A244216 1,1
%A A244216 _Antti Karttunen_, Jun 23 2014