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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.
3
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.
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.
Related or similar permutations: A252755, A267111, A269855.
Sequence in context: A188706 A304408 A048767 * A284457 A365656 A182944
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 07 2016
STATUS
approved