OFFSET
1,1
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..319.
Y. More, Problem 11165, Amer. Math. Monthly, 112 (2005), 568.
FORMULA
a(2^j) = 2*a(2^j-1) + 2 (resp. + 4) if j is even (resp. odd). - M. F. Hasler, Feb 25 2008
a(n) = 2*Sum_{i=1..n} A137822(i). - M. F. Hasler, Mar 16 2008
{n: A137993(n-1) = 0}. - R. J. Mathar, Jul 07 2009
MAPLE
A107755 := proc(n) option remember ; local a; if n = 1 then 2; else for a from A107755(n-1)+1 do if add(A000108(k), k=1..a) mod 3 = 0 then RETURN(a) ; fi ; od: fi ; end: # R. J. Mathar, Feb 25 2008
c:=n->binomial(2*n, n)/(n+1): s:=0: for n from 1 to 1500 do s:=s+c(n): a[n]:=s mod 3: od: A:=[seq(a[n], n=1..1500)]: p:=proc(n) if A[n]=0 then n else fi end: seq(p(n), n=1..1500); # Emeric Deutsch, Jun 12 2005
MATHEMATICA
s0 = s2 = {}; s = 0; Do[s = Mod[s + (2 n)!/n!/(n + 1)!, 3]; Switch[ Mod[s, 3], 0, AppendTo[s0, n], 2, AppendTo[s2, n]], {n, 1055}]; s0 (* Robert G. Wilson v, Jun 14 2005 *)
Flatten[Position[Accumulate[CatalanNumber[Range[1100]]], _?(Divisible[ #, 3]&)]] (* Harvey P. Dale, Feb 07 2016 *)
PROG
(PARI) n=0; s=Mod(0, 3); A107755=vector(100, i, if( bitand(i, i-1), while(n++ && s+=binomial(2*n, n)/(n+1), ), s=Mod(0, 3); n=2*n+2+(log(i+.5)\log(2)%2)*2 ); /*print1(n", "); */ n) \\ M. F. Hasler, Feb 25 2008
(PARI) A107755(n)=sum( i=1, n, A137822(i) )*2 /* allows computation of a(10^4) in one second */ \\ M. F. Hasler, Mar 16 2008
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 11 2005
EXTENSIONS
More terms from Emeric Deutsch, Jun 12 2005
Corrected & extended by M. F. Hasler and R. J. Mathar, Feb 25 2008
STATUS
approved