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A087734
a(n) = f(f(n)), where f() = A035327().
5
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 3, 0, 1, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 0, 1, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 0, 1, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
OFFSET
0,11
LINKS
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
FORMULA
From Mikhail Kurkov, Sep 29 2019: (Start)
Some conjectures:
a(n) = n - Sum_{k=A063250(n)..A000523(n)} 2^k = n - 2^(A000523(n)+1) + 2^A063250(n) for n>0 with a(0)=0.
G.f.: 1/(1-x) * Sum_{j>=0} (2^j)*((x^(2^j))/(1+x^(2^j)) - (1-x^(2^j)) * Sum_{k>=1} x^((2^j)*(2^k-1))).
a(n) = 2*a(floor(n/2)) + n mod 2 - A036987(n) for n>1 with a(0)=a(1)=0.
a(n) = (1 - A036987(n-1))*(1 + A063250(n) - A063250(n-1))*(1 + a(n-1)) for n>0 with a(0)=0. (End)
MAPLE
a:= n-> ((i->Bits[Nand](i$2))@@2)(n):
seq(a(n), n=0..100); # Alois P. Heinz, Sep 29 2019
MATHEMATICA
{0}~Join~Array[Nest[BitXor[#, 2^IntegerPart[Log2@ # + 1] - 1] &, #, 2] /. -1 -> 0 &, 81] (* Michael De Vlieger, Sep 29 2019 *)
CROSSREFS
Sequence in context: A342315 A063890 A156439 * A073644 A123343 A054439
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 01 2003
STATUS
approved