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A245599
Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.
2
1, 11, 91, 731, 5851, 46811, 374491, 2995931, 23967451, 191739611, 1533916891, 12271335131, 98170681051, 785365448411, 6282923587291, 50263388698331, 402107109586651, 3216856876693211, 25734855013545691, 205878840108365531, 1647030720866924251, 13176245766935394011
OFFSET
1,2
COMMENTS
Sequence consists of all numbers with binary representation 1(011)*.
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)
EXAMPLE
A030101(11) = 13, A030109(11) = 6, and 13 XOR 6 = (1101)_2 XOR (0110)_2 = (1011)_2 = 11, so 11 is in the sequence.
MATHEMATICA
a[n_] := (5*8^n - 12)/28; Array[a, 20] (* Giovanni Resta, Apr 25 2020 *)
PROG
(PARI) Vec(x*(1 + 2*x) / ((1 - x)*(1 - 8*x)) + O(x^20)) \\ Colin Barker, Apr 25 2020
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Muehlfeld, Jul 27 2014
EXTENSIONS
More terms from Giovanni Resta, Apr 25 2020
STATUS
approved