cp's OEIS Frontend

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.

A107756 Numbers k such that Sum_{j=1..k} Catalan(j) == 1 (mod 3).

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%I A107756 #16 Aug 26 2022 16:52:19
%S A107756 1,4,5,6,7,10,13,14,15,16,17,18,19,20,21,22,23,24,25,28,31,32,33,34,
%T A107756 37,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
%U A107756 62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,82,85,86,87,88,91,94,95
%N A107756 Numbers k such that Sum_{j=1..k} Catalan(j) == 1 (mod 3).
%H A107756 Y. More, <a href="https://www.jstor.org/stable/30037533">Problem 11165</a>, Amer. Math. Monthly, 112 (2005), 568.
%F A107756 Equivalently, numbers k such that base-3 expansion of k+1 contains a 2.
%t A107756 Select[ Range[ 100], Mod[ Sum[(2 n)!/n!/(n + 1)!, {n, #}], 3] == 1 &] (* _Robert G. Wilson v_, Jun 14 2005 *)
%t A107756 Position[Accumulate[CatalanNumber[Range[100]]],_?(Mod[#,3]==1&)]//Flatten (* _Harvey P. Dale_, Aug 26 2022 *)
%Y A107756 Cf. A000108, A107755, A107757.
%Y A107756 Equals A074940 - 1.
%K A107756 nonn,easy
%O A107756 1,2
%A A107756 _N. J. A. Sloane_, Jun 11 2005