A277812 -id:A277812 - cp's OEIS frontend

A277813 a(n) = A115384(A277812(n)) = index of the row where n is located in array A277880.

1, 2, 1, 3, 2, 1, 4, 5, 3, 2, 6, 1, 7, 8, 4, 9, 5, 3, 10, 2, 11, 12, 6, 1, 13, 14, 7, 15, 8, 4, 16, 17, 9, 5, 18, 3, 19, 20, 10, 2, 21, 22, 11, 23, 12, 6, 24, 1, 25, 26, 13, 27, 14, 7, 28, 29, 15, 8, 30, 4, 31, 32, 16, 33, 17, 9, 34, 5, 35, 36, 18, 3, 37, 38, 19, 39, 20, 10, 40, 2, 41, 42, 21, 43, 22, 11, 44, 45, 23, 12, 46, 6, 47, 48, 24, 1, 49, 50

Offset: 1

Antti Karttunen, Nov 03 2016

a(n) = index of the first odious number which is encountered when we start from k = n and iterate the map k -> A003188(A006068(k)/2).
Ordinal transform of A277822.
This works as a left inverse of A000069 like also does A115384.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Cf. A000069, A001969, A003188, A006068, A010060, A115384, A268671, A277812, A277880, A277822.

Cf. A003945 (the positions of 1's in this sequence).

(define (A277813 n) (A115384 (A277812 n)))

a(n) = A115384(A277812(n)).
Other identities. For all n >= 1:
a(A000069(n)) = n.
a(n) = a(floor(n/2)) when A010060(n) = 0.

A277808 a(n) = number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 6, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4

Offset: 1

Antti Karttunen, Nov 03 2016

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

One less than A277822.
A left inverse of A003945.
Cf. A277812 (gives the odious number where such an iteration is finished at when starting from k=n).
Cf. A000069, A001969, A001511, A003188, A006068, A010059, A010060, A245710, A268389.

a(n) = A010059(n) * A001511(n).
If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = 0, otherwise a(n) = 1 + a(A003188(A006068(n)/2)).
Other identities:
For all n >= 0, a(A003945(n)) = n.

cp's OEIS Frontend

A277813 a(n) = A115384(A277812(n)) = index of the row where n is located in array A277880.

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