A277812 a(n) = the first odious number encountered when starting from k = n and iterating the map k -> A003188(A006068(k)/2).

1, 2, 1, 4, 2, 1, 7, 8, 4, 2, 11, 1, 13, 14, 7, 16, 8, 4, 19, 2, 21, 22, 11, 1, 25, 26, 13, 28, 14, 7, 31, 32, 16, 8, 35, 4, 37, 38, 19, 2, 41, 42, 21, 44, 22, 11, 47, 1, 49, 50, 25, 52, 26, 13, 55, 56, 28, 14, 59, 7, 61, 62, 31, 64, 32, 16, 67, 8, 69, 70, 35, 4, 73, 74, 37, 76, 38, 19, 79, 2, 81, 82, 41, 84, 42, 21, 87, 88, 44, 22, 91, 11, 93, 94, 47, 1, 97, 98, 49, 100

Offset: 1

Author

Antti Karttunen, Nov 03 2016

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A000069, A001969, A000265, A003188, A006068, A010060, A268669, A277813.

Cf. A277808 (gives the number of such iterations needed to reach a(n) from n).

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

Formula

If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = n, otherwise a(n) = a(A003188(A006068(n)/2)).

Other identities:

a(n) = A000069(A277813(n)).

If A010060(n) = 0 [when n is one of the evil numbers, A001969], then a(n)= a(A000265(n)) [the trailing zeros in binary expansion of n do not affect the result].

For all n >= 1, a(A000069(n)) = A000069(n). [By definition].

For all n > 1, a(A001969(n)) < A001969(n).