A269855 -id:A269855 - cp's OEIS frontend

A269851 a(0) = 1, a(A087686(1+n)) = 2*a(n), a(A088359(n)) = A250469(a(n)), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001.

1, 2, 4, 3, 8, 9, 5, 6, 16, 21, 25, 7, 18, 15, 10, 12, 32, 45, 55, 49, 11, 42, 51, 35, 50, 27, 14, 36, 33, 30, 20, 24, 64, 93, 115, 91, 121, 13, 90, 123, 125, 77, 110, 147, 65, 98, 39, 22, 84, 105, 85, 102, 87, 70, 100, 57, 54, 28, 72, 69, 66, 60, 40, 48, 128, 189, 235, 203, 187, 169, 17, 186, 267, 305, 217, 143, 230

Offset: 0

Antti Karttunen, Mar 07 2016

nonn

Permutation of natural numbers obtained from the sieve of Eratosthenes, combined with the permutation obtained from Hofstadter-Conway $10000 sequence (A004001). Note the indexing: Domain starts from 0, range from 1.

Inverse: A269852.
Cf. A004001, A087686, A088359, A093879, A250469.
Related or similar permutations: A252755, A267111, A269855.

a(0) = 1, a(1) = 2, for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 2*a(n - A004001(n)), otherwise [when n is in A088359], a(n) = A250469(a(A004001(n)-1)).
As a composition of related permutations:
a(n) = A252755(A267111(n)).
Other identities. For all n >= 0:
a(2^n) = 2^(n+1).

A269856 Permutation of natural numbers: a(1) = 0, a(2) = 1, a(2n) = A001969(1+a(n)), a(2n+1) = A000069(1+a(A268674(2n+1))).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 6, 7, 9, 16, 10, 32, 17, 11, 12, 64, 15, 128, 18, 13, 33, 256, 20, 14, 65, 19, 34, 512, 23, 1024, 24, 21, 129, 22, 30, 2048, 257, 35, 36, 4096, 27, 8192, 66, 25, 513, 16384, 40, 28, 29, 31, 130, 32768, 39, 26, 68, 37, 1025, 65536, 46, 131072, 2049, 67, 48, 38, 43, 262144, 258, 41, 45, 524288, 60

Offset: 1

Antti Karttunen, Mar 07 2016

nonn

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

Inverse: A269855.
Cf. A000069, A001969, A268674.
Related or similar permutations: A003188, A252756, A269852.

a(1) = 0, a(2) = 1, a(2n) = A001969(1+a(n)), a(2n+1) = A000069(1+a(A268674(2n+1))).
As a composition of other permutations:
a(n) = A003188(A252756(n)).

cp's OEIS Frontend

A269851 a(0) = 1, a(A087686(1+n)) = 2*a(n), a(A088359(n)) = A250469(a(n)), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001.

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