A265734 Permutation of nonnegative integers: a(n) = n + floor(n/5)*(-1)^(n mod 5).

0, 1, 2, 3, 4, 6, 5, 8, 7, 10, 12, 9, 14, 11, 16, 18, 13, 20, 15, 22, 24, 17, 26, 19, 28, 30, 21, 32, 23, 34, 36, 25, 38, 27, 40, 42, 29, 44, 31, 46, 48, 33, 50, 35, 52, 54, 37, 56, 39, 58, 60, 41, 62, 43, 64, 66, 45, 68, 47, 70, 72, 49, 74, 51, 76, 78, 53, 80

Offset: 0

Author

Bruno Berselli, Dec 15 2015 - based on an idea by Paul Curtz

Keywords

• nonn
• easy

Examples

			------------------------------------------------------------------------
0, 1, 2, 3, 4, 5,  6, 7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ...
+  +  +  +  +  +   +  +   +   +   +   +   +   +   +   +   +   +   +
0, 0, 0, 0, 0, 1, -1, 1, -1,  1,  2, -2,  2, -2,  2,  3, -3,  3, -3, ...
------------------------------------------------------------------------
0, 1, 2, 3, 4, 6,  5, 8,  7, 10, 12,  9, 14, 11, 16, 18, 13, 20, 15, ...
------------------------------------------------------------------------
		

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).
• Index entries for permutations of the positive (or nonnegative) integers.

Crossrefs

Cf. A001477.

Cf. A064455: n+floor(n/2)*(-1)^(n mod 2).

Cf. A265667: n+floor(n/3)*(-1)^(n mod 3).

Cf. A265888: n+floor(n/4)*(-1)^(n mod 4)

Programs

Magma

[n+Floor(n/5)*(-1)^(n mod 5): n in [0..80]];

Mathematica

Table[n + Floor[n/5] (-1)^Mod[n, 5], {n, 0, 80}]

Sage

[n+floor(n/5)*(-1)^mod(n, 5) for n in (0..80)]

Formula

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 3*x^5 + 4*x^6 + x^7 + 2*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).

a(n) = 2*a(n-5) - a(n-10).

a(5*k+r) = (5+(-1)^r)*k + r, where r=0..4.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*(1/(2*sqrt(2))-1/(3*sqrt(3))) + log(2)/6. - Amiram Eldar, Mar 30 2023