A267100 Self-inverse permutation of natural numbers: a(1) = 1, a(A080147(n)) = A080148(n), a(A080148(n)) = A080147(n).

1, 3, 2, 6, 7, 4, 5, 10, 12, 8, 13, 9, 11, 16, 18, 14, 21, 15, 24, 25, 17, 26, 29, 19, 20, 22, 30, 33, 23, 27, 35, 37, 28, 40, 31, 42, 32, 44, 45, 34, 50, 36, 51, 38, 39, 53, 55, 57, 59, 41, 43, 60, 46, 62, 47, 65, 48, 66, 49, 52, 68, 54, 70, 71, 56, 58, 74, 61, 77, 63, 64, 78, 79, 67, 80, 82, 69, 72, 73, 75, 84, 76, 87, 81

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1; for n > 1, if prime(n) mod 4 = 1, then a(n) = A080148(A267097(n)), otherwise a(n) = A080147(A267098(n)).

Other identities. For all n >= 1:

a(n) = A000720(A267101(n)).

Prog

(Scheme, two variants)
(define (A267100 n) (A000720 (A267101 n)))
(define (A267100 n) (cond ((<= n 1) n) ((= 1 (modulo (A000040 n) 4)) (A080148 (A267097 n))) (else (A080147 (A267098 n)))))

Crossrefs

Cf. A000040, A000720, A080147, A080148, A267101, A267097, A267098, A267099.

Cf. also A267107 (a more recursed variant).

Sequence in context: A207636 A125764 A023897 * A178754 A276446 A100527

Adjacent sequences: A267097 A267098 A267099 * A267101 A267102 A267103

Keyword

nonn

Author

Antti Karttunen, Feb 01 2016

Status

approved