A245179 Numbers of the form 2^k+3 or 3*2^k+1, k >= 2.

7, 11, 13, 19, 25, 35, 49, 67, 97, 131, 193, 259, 385, 515, 769, 1027, 1537, 2051, 3073, 4099, 6145, 8195, 12289, 16387, 24577, 32771, 49153, 65539, 98305, 131075, 196609, 262147, 393217, 524291, 786433, 1048579, 1572865, 2097155, 3145729, 4194307, 6291457

Offset: 1

Author

N. J. A. Sloane, Jul 17 2014

Keywords

• nonn
• easy

Comments

Numbers whose binary expansion is 10..011 or 110..01.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).

Crossrefs

Essentially the union of A062709 and A181565. Cf. A245178.

Programs

Magma

&cat [[3*2^i+1,2^(i+2)+3]: i in [1..30]]; // Bruno Berselli, Jul 23 2014

Mathematica

CoefficientList[Series[- (14 x^3 + 8 x^2 - 11 x - 7)/((x - 1) (x + 1) (2 x^2 - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 23 2014 *)
LinearRecurrence[{0,3,0,-2},{7,11,13,19},50] (* Harvey P. Dale, Mar 05 2015 *)

Formula

a(2k) = 2^(k+2)+3, a(2k+1) = 3*2^(k+1)+1. - N. J. A. Sloane, Jul 19 2014

a(n) = 3*a(n-2)-2*a(n-4). G.f.: -x*(14*x^3+8*x^2-11*x-7) / ((x-1)*(x+1)*(2*x^2-1)). - Colin Barker, Jul 19 2014