A065259 A057114 conjugated with A059893, inverse of A065260.

3, 1, 7, 2, 11, 5, 15, 4, 19, 9, 23, 6, 27, 13, 31, 8, 35, 17, 39, 10, 43, 21, 47, 12, 51, 25, 55, 14, 59, 29, 63, 16, 67, 33, 71, 18, 75, 37, 79, 20, 83, 41, 87, 22, 91, 45, 95, 24, 99, 49, 103, 26, 107, 53, 111, 28, 115, 57, 119, 30, 123, 61, 127, 32, 131, 65, 135, 34, 139

Offset: 1

Author

Antti Karttunen, Oct 28 2001

Keywords

• nonn
• easy

Examples

			G.f. = 3*x + x^2 + 7*x^3 + 2*x^4 + 11*x^5 + 5*x^6 + 15*x^7 + 4*x^8 + ...
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for sequences that are permutations of the natural numbers
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Programs

PARI

Vec(x*(3+x+7*x^2+2*x^3+5*x^4+3*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)^2) + O(x^100)) \\ Colin Barker, Oct 29 2016

PARI

{a(n) = if( n%2, 2*n+1, n%4, n-1, n/2)}; /* Michael Somos, Nov 06 2016 */

Formula

a(n) = A059893(A057114(A059893(n))).

a(2*k+1) = 4*k+3, a(4*k+2) = 4*k+1, a(4*k+4) = 2*k+2. - Ralf Stephan, Jun 10 2005

a(n) = (11*n+2-(5*n+6)*(-1)^n+(n-2)*(1+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/8. - Luce ETIENNE, Oct 29 2016

From Colin Barker, Oct 29 2016: (Start)

a(n) = 2*a(n-4) - a(n-8) for n>8.

G.f.: x*(3 + x + 7*x^2 + 2*x^3 + 5*x^4 + 3*x^5 + x^6)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2). (End)