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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to binary expansion of n

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).

Prog

(Scheme, with memoization-macro definec)
(definec (A277812 n) (if (= 1 (A010060 n)) n (A277812 (A003188 (/ (A006068 n) 2)))))

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).

Sequence in context: A239829 A210034 A074586 * A134586 A135287 A359803

Adjacent sequences: A277809 A277810 A277811 * A277813 A277814 A277815

Keyword

nonn,base

Author

Antti Karttunen, Nov 03 2016

Status

approved