A257734 Permutation of natural numbers: a(1) = 1, a(lucky(n)) = ludic(1+a(n-1)), a(unlucky(n)) = nonludic(a(n)), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505, and ludic = A003309, nonludic = A192607.

1, 4, 2, 9, 6, 16, 7, 12, 3, 26, 14, 20, 25, 8, 13, 38, 22, 31, 36, 15, 61, 21, 54, 33, 17, 45, 51, 24, 81, 32, 41, 73, 5, 48, 27, 62, 119, 69, 35, 105, 46, 57, 47, 96, 10, 65, 39, 82, 83, 151, 115, 92, 50, 135, 63, 76, 64, 124, 18, 86, 55, 106, 23, 108, 189, 146, 43, 118, 193, 68, 169, 84, 91, 100, 149, 85, 156, 28, 179, 111, 74, 136, 34

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1; for n > 1: if A145649(n) = 1 [i.e., if n is lucky], then a(n) = A003309(1+a(A109497(n)-1)), otherwise a(n) = A192607(a(n-A109497(n))).

As a composition of other permutations:

a(n) = A255421(A257732(n)).

a(n) = A237126(A257725(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A257734 n) (cond ((= 1 n) n) ((= 1 (A145649 n)) (A003309 (+ 1 (A257734 (- (A109497 n) 1))))) (else (A192607 (A257734 (- n (A109497 n)))))))
;; Alternatively, by composing other permutations:
(define (A257734 n) (A255421 (A257732 n)))
(define (A257734 n) (A237126 (A257725 n)))

Crossrefs

Inverse: A257733.

Cf. A000959, A050505, A003309, A109497, A145649, A192607.

Related or similar permutations: A237126, A255421, A257725, A257732.

Cf. also A256486, A256487.

Sequence in context: A182702 A282600 A326845 * A257732 A351164 A101690

Adjacent sequences: A257731 A257732 A257733 * A257735 A257736 A257737

Keyword

nonn

Author

Antti Karttunen, May 06 2015

Status

approved