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

0,2

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for Hofstadter-type sequences

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences generated by sieves

Formula

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).

Prog

(Scheme, with memoization-macro definec)
(definec (A269851 n) (cond ((<= n 1) (+ 1 n)) ((zero? (A093879 (- n 1))) (* 2 (A269851 (- n (A004001 n))))) (else (A250469 (A269851 (+ -1 (A004001 n)))))))

Crossrefs

Inverse: A269852.

Cf. A004001, A087686, A088359, A093879, A250469.

Related or similar permutations: A252755, A267111, A269855.

Sequence in context: A188706 A304408 A048767 * A284457 A365656 A182944

Adjacent sequences: A269848 A269849 A269850 * A269852 A269853 A269854

Keyword

nonn

Author

Antti Karttunen, Mar 07 2016

Status

approved