A267112 -id:A267112 - cp's OEIS frontend

A276446 Permutation of natural numbers: a(1) = 1; a(A000069(1+n)) = A088359(a(n)), a(A001969(1+n)) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.

1, 3, 2, 6, 7, 4, 5, 11, 14, 15, 13, 8, 9, 10, 12, 20, 26, 30, 25, 31, 28, 23, 29, 16, 17, 18, 21, 19, 24, 27, 22, 37, 47, 57, 46, 62, 55, 44, 56, 63, 59, 50, 60, 41, 53, 61, 52, 32, 33, 34, 38, 35, 42, 48, 39, 36, 45, 54, 43, 58, 49, 40, 51, 70, 85, 105, 84, 120, 103, 82, 104, 126, 117, 98, 118, 79, 101, 119, 100, 127, 122, 108, 123, 89

Offset: 1

Antti Karttunen, Sep 03 2016

Inverse: A276445.
Cf. A000069, A001969, A004001, A010060, A087686, A088359, A115384, A245710.
Similar or related permutations: A006068, A267112, A276444.

(definec (A276446 n) (cond ((< n 2) n) ((zero? (A010060 n)) (A087686 (+ 1 (A276446 (A245710 n))))) (else (A088359 (A276446 (- (A115384 n) 1))))))

a(1) = 1, and for n > 1, if A010060(n) = 1 [when n is one of the odious numbers, A000069], a(n) = A088359(a(A115384(n)-1)), otherwise a(n) = A087686(1+a(A245710(n))).
As a composition of other permutations:
a(n) = A267112(A006068(n)).

A269852 Permutation of natural numbers: a(1) = 0, after which, a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(A268674(2n+1))).

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 11, 4, 5, 14, 20, 15, 37, 26, 13, 8, 70, 12, 135, 30, 9, 47, 264, 31, 10, 85, 25, 57, 521, 29, 1034, 16, 28, 156, 23, 27, 2059, 292, 46, 62, 4108, 21, 8205, 105, 17, 557, 16398, 63, 19, 24, 22, 191, 32783, 56, 18, 120, 55, 1079, 65552, 61, 131089, 2114, 84, 32, 44, 60, 262162, 348, 59, 53

Offset: 1

Antti Karttunen, Mar 07 2016

nonn

Note the indexing: Domain starts from 1, range from 0.

Inverse: A269851.
Cf. A004001, A087686, A088359, A268674.
Related or similar permutations: A252756, A267112, A269856.

a(1) = 0; after which, for even n, a(n) = A087686(1+a(n/2)), and for odd n, a(n) = A088359(a(A268674(n))).
Other identities. For all n >= 1:
a(2^n) = 2^(n-1).
As a composition of other permutations:
a(n) = A267112(A252756(n)).

cp's OEIS Frontend

A276446 Permutation of natural numbers: a(1) = 1; a(A000069(1+n)) = A088359(a(n)), a(A001969(1+n)) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.

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