A118113 Even Fibbinary numbers + 1; also 2*Fibbinary(n) + 1.

1, 3, 5, 9, 11, 17, 19, 21, 33, 35, 37, 41, 43, 65, 67, 69, 73, 75, 81, 83, 85, 129, 131, 133, 137, 139, 145, 147, 149, 161, 163, 165, 169, 171, 257, 259, 261, 265, 267, 273, 275, 277, 289, 291, 293, 297, 299, 321, 323, 325, 329, 331, 337, 339, 341, 513, 515, 517

Offset

0,2

Comments

m for which binomial(3*m-2,m) (see A117671) is odd, since by Kummer's theorem that happens exactly when the binary expansions of m and 2*m-2 have no 1 bit at the same position in each, and so m odd and no 11 bit pairs except optionally the least significant 2 bits. - Kevin Ryde, Jun 14 2025

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A022340(n) + 1.

a(n) = 2*A003714(n) + 1.

Solutions to {x : binomial(3x,x) mod (x+1) != 0 } are given in A022341. The corresponding values of binomial(3x,x) mod (x+1) are given here.

Maple

F:= combinat[fibonacci]:
b:= proc(n) local j;
      if n=0 then 0
    else for j from 2 while F(j+1)<=n do od;
         b(n-F(j))+2^(j-2)
      fi
    end:
a:= n-> 2*b(n)+1:
seq(a(n), n=0..70);  # Alois P. Heinz, Aug 03 2012

Mathematica

Select[Table[Mod[Binomial[3*k, k], k+1], {k, 1200}], #>0&]

Crossrefs

Cf. A000108, A118112, A022341.

Cf. A003714 (Fibbinary numbers), A022340 (even Fibbinary numbers).

Cf. A117671, A263190, A171791, A263075.

Sequence in context: A036696 A111039 A114512 * A258165 A076193 A056533

Adjacent sequences: A118110 A118111 A118112 * A118114 A118115 A118116

Keyword

nonn,easy

Author

Labos Elemer, Apr 13 2006

Extensions

New definition from T. D. Noe, Dec 19 2006

Status

approved