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A359312
a(1) = 1; for n >= 1, a(2*n) = A000005(a(n)), a(2*n + 1) = A000005(a(n)) + 1.
0
1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2
OFFSET
1,3
FORMULA
Sum_{i = 2^k..2^(k + 1) - 1} a(i) = 5*2^(k - 1) - 2, for k >= 1.
a(2^k) = 1.
EXAMPLE
a(1) = 1;
a(2) = A000005(a(1)) = 1;
a(3) = A000005(a(1)) + 1 = 2;
a(4) = A000005(a(2)) = 1;
a(5) = A000005(a(2)) + 1 = 2;
and so on.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = If[EvenQ[n], DivisorSigma[0, a[n/2]], DivisorSigma[0, a[(n - 1)/2]] + 1]; Array[a, 100] (* Amiram Eldar, Dec 25 2022 *)
CROSSREFS
Sequence in context: A144016 A376109 A354582 * A179868 A104232 A072086
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Dec 25 2022
STATUS
approved