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A118113
Even Fibbinary numbers + 1; also 2*Fibbinary(n) + 1.
13
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
a(n) = A022340(n) + 1 = 2*A003714(n) + 1.
LINKS
FORMULA
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. A003714 (Fibbinary numbers), A022340 (even Fibbinary numbers).
Sequence in context: A036696 A111039 A114512 * A258165 A076193 A056533
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 13 2006
EXTENSIONS
New definition from T. D. Noe, Dec 19 2006
STATUS
approved