A214865 n such that n XOR 9 = n - 9.

9, 11, 13, 15, 25, 27, 29, 31, 41, 43, 45, 47, 57, 59, 61, 63, 73, 75, 77, 79, 89, 91, 93, 95, 105, 107, 109, 111, 121, 123, 125, 127, 137, 139, 141, 143, 153, 155, 157, 159, 169, 171, 173, 175, 185, 187, 189, 191, 201, 203, 205, 207, 217, 219, 221, 223, 233, 235, 237, 239, 249, 251

Offset: 1

Author

Brad Clardy, Mar 09 2013

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A214863, A016825, A132429.

Programs

Magma

XOR := func;
m:=9;
for n in [1 .. 500] do
      if (XOR(n, m) eq n-m) then n; end if;
end for;

Mathematica

CoefficientList[Series[x*(9 + 2*x + 2*x^2 + 2*x^3 + x^4)/((1 + x)*(x^2 + 1)*(x - 1)^2), {x,0,50}], x] (* G. C. Greubel, Feb 22 2017 *)

PARI

x='x+O('x^50); Vec(x*(9+2*x+2*x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 )) \\ G. C. Greubel, Feb 22 2017

Formula

a(n) = 4*n + 6 + (-1)^n + 2*(-1)^((2*n+(-1)^n-1)/4) for n>=0.

a(n) = A016825(n+1) + A132429(n) for n>=0.

G.f. x*(9+2*x+2*x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Mar 10 2013

a(n+4) = a(n) + 16. - Alexander R. Povolotsky, Mar 15 2013