A277901 If A010060(n) = 1, a(n) = A065621(A115384(n)), otherwise a(n) = A048724(a(floor(n/2))).

1, 2, 3, 7, 6, 5, 4, 13, 9, 10, 14, 15, 11, 8, 12, 25, 23, 27, 26, 30, 31, 28, 18, 17, 21, 22, 29, 19, 24, 20, 16, 49, 43, 57, 50, 45, 55, 52, 46, 34, 61, 62, 33, 59, 36, 54, 56, 51, 41, 42, 63, 47, 58, 39, 44, 37, 53, 40, 38, 60, 35, 32, 48, 97, 83, 125, 98, 75, 103, 100, 86, 119, 109, 110, 89, 107, 92, 114

Offset

1,2

Comments

a(n) gives the number that is in the same position in array A277820 as where n is located in array A277880.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = A065621(A115384(n)), otherwise a(n) = A048724(a(floor(n/2))).

As a composition of other permutations:

a(n) = A277820(A277881(n)).

Other identities. For all n >= 1:

A010060(a(n)) = A010060(n). [Preserves the parity of binary weight.]

a(A000069(n)) = A065621(n).

a(A003945(n)) = A001317(n).

a(A129771(n)) = A277823(n).

a(2*A129771(n)) = A277825(n).

Example

The top left corner of array A277880 is:
   1,  3,  6, 12
   2,  5, 10, 20
   4,  9, 18, 36
   7, 15, 30, 60
   8, 17, 34, 68
while the top left corner of A277820 is:
   1,  3,  5, 15
   2,  6, 10, 30
   7,  9, 27, 45
   4, 12, 20, 60
  13, 23, 57, 75
thus a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 7, a(5) = 6, a(6) = 5, a(7) = 4, a(8) = 13, a(9) = 9, a(12) = 15 and a(15) = 12.

Prog

(Scheme, with memoization-macro definec)
(definec (A277901 n) (if (= 1 (A010060 n)) (A065621 (A115384 n)) (A048724 (A277901 (floor->exact (/ n 2))))))
(define (A277901 n) (A277820 (A277881 n)))

Crossrefs

Inverse: A277902.

Cf. A000069, A001969, A010060, A048724, A065621, A115384, A129771, A277823, A277825.

Related permutations and arrays: A277820, A277880, A277881.

Sequence in context: A277819 A098287 A115304 * A277902 A098285 A019585

Adjacent sequences: A277898 A277899 A277900 * A277902 A277903 A277904

Keyword

nonn,base

Author

Antti Karttunen, Nov 03 2016

Status

approved