A245599 Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.

1, 11, 91, 731, 5851, 46811, 374491, 2995931, 23967451, 191739611, 1533916891, 12271335131, 98170681051, 785365448411, 6282923587291, 50263388698331, 402107109586651, 3216856876693211, 25734855013545691, 205878840108365531, 1647030720866924251, 13176245766935394011

Offset: 1

Author

Reinhard Muehlfeld, Jul 27 2014

Keywords

• nonn
• base
• easy

Comments

Sequence consists of all numbers with binary representation 1(011)*.

Examples

			A030101(11) = 13,  A030109(11) = 6, and 13 XOR 6 = (1101)_2 XOR (0110)_2 = (1011)_2 = 11, so 11 is in the sequence.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1001
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A007088, A030109, A030101.

Programs

Mathematica

a[n_] := (5*8^n - 12)/28; Array[a, 20] (* Giovanni Resta, Apr 25 2020 *)

PARI

Vec(x*(1 + 2*x) / ((1 - x)*(1 - 8*x)) + O(x^20)) \\ Colin Barker, Apr 25 2020

Formula

a(n) = 1(011)^(n-1) in binary representation.

a(n) = (5*8^n - 12)/28. - Giovanni Resta, Apr 25 2020

From Colin Barker, Apr 25 2020: (Start)

G.f.: x*(1 + 2*x) / ((1 - x)*(1 - 8*x)).

a(n) = 9*a(n-1) - 8*a(n-2) for n>2.

(End)

Extensions

More terms from Giovanni Resta, Apr 25 2020