A133256 a(4*n+1) = 4*n+1, a(4*n+2) = 4*n+2, a(4*n+3) = 4*n+4, a(4*n+4) = 4*n+3.

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

Offset: 1

Author

Paul Curtz, Oct 15 2007

Keywords

• nonn

Comments

A permutation of the positive integers, swapping consecutive values congruent to 3 and 4 (mod 4). - Franklin T. Adams-Watters, Jan 22 2012.

This is the lexicographically earliest sequence of distinct positive integers such that no polynomial of degree d can be fitted to d+2 consecutive terms (equivalently, such that no iterated difference is zero). - Pontus von Brömssen, Dec 26 2021

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A103889.

Programs

Mathematica

Table[Which[Mod[n,4]==3,n+1,Divisible[n,4],n-1,True,n],{n,40}] (* or *) Partition[Range[40],4]/.{a_,b_,c_,d_}->{a,b,d,c}//Flatten (* Harvey P. Dale, Aug 29 2016 *)

Formula

From Chai Wah Wu, Sep 10 2020: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.

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

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/4 - log(2)/2. - Amiram Eldar, Jan 31 2023

Extensions

Definition fixed and offset changed by Franklin T. Adams-Watters, Jan 22 2012