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Indices of Catalan numbers that are == 1 mod 3 (cf. A000108).
1

%I #10 Jun 30 2020 16:13:07

%S 1,11,12,13,29,30,31,35,36,37,83,84,85,89,90,91,107,108,109,119,120,

%T 121,245,246,247,251,252,253,269,270,271,281,282,283,323,324,325,335,

%U 336,337,353,354,355,359,360,361,731,732,733,737,738,739,755

%N Indices of Catalan numbers that are == 1 mod 3 (cf. A000108).

%H Robert Israel, <a href="/A111019/b111019.txt">Table of n, a(n) for n = 1..10000</a>

%F a(3k) = a(3k-1)+1 and a(3k+1) = a(3k-1)+2 for k >= 1. - _Robert Israel_, Jun 30 2020

%p filter:= proc(n) local L1, L2, L3;

%p L1:= convert(2*n, base, 3);

%p L2:= convert(n, base, 3);

%p L3:= convert(n-1, base, 3);

%p mul(binomial(L1[i], L2[i]), i=1..nops(L2)) - mul(binomial(L1[i], L3[i]), i=1..nops(L3)) mod 3 = 1

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Jun 30 2020

%t Flatten[Position[CatalanNumber[Range[1000]],_?(Mod[#,3]==1&)]] (* _Harvey P. Dale_, Jun 19 2014 *)

%Y Cf. A000108, A111020.

%K nonn,look

%O 1,2

%A _Robert G. Wilson v_, Sep 09 2005