A081868 Numbers k such that Sum_{j=1..k} (binomial(2*j,j) mod 3) is even.

1, 2, 3, 10, 11, 28, 29, 36, 37, 38, 39, 82, 83, 90, 91, 92, 93, 108, 109, 110, 111, 118, 119, 244, 245, 252, 253, 254, 255, 270, 271, 272, 273, 280, 281, 324, 325, 326, 327, 334, 335, 352, 353, 360, 361, 362, 363, 730, 731, 738, 739, 740, 741, 756, 757, 758

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

  N:= 10000: # to get all terms <= N
alpha:= 2:
beta:= 0:
t:= 0:
A[1]:= 1:
count:= 1:
for i from 2 to N do
  d:= padic:-ordp(4 - 2/i, 3);
  beta:= beta + d;
  alpha:= alpha * (4-2/i)/3^d mod 3;
  if beta = 0 then
     t:= t + alpha mod 2;
  fi;
  if t = 0 then
     count:= count+1;
     A[count]:= i;
  fi
od:
seq(A[i], i=1..count); # Robert Israel, May 05 2014

Mathematica

Select[Range[800], EvenQ[Sum[Mod[Binomial[2j, j], 3], {j, #}]]&] (* Harvey P. Dale, Jul 23 2023 *)

Prog

(PARI) isok(n) = ! (sum(k=1, n, binomial(2*k, k) % 3) % 2); \\ Michel Marcus, Dec 04 2013

Crossrefs

Sequence in context: A281366 A324921 A307034 * A212103 A193652 A345369

Adjacent sequences: A081865 A081866 A081867 * A081869 A081870 A081871

Keyword

nonn

Author

Benoit Cloitre, Apr 12 2003

Extensions

More terms from Michel Marcus, Dec 04 2013

Status

approved