A104706 First terms in the rearrangements of integer numbers (see comments).

1, 2, 3, 1, 4, 5, 1, 2, 6, 1, 7, 3, 1, 2, 8, 1, 9, 4, 1, 2, 10, 1, 3, 11, 1, 2, 5, 1, 12, 13, 1, 2, 3, 1, 4, 6, 1, 2, 14, 1, 15, 3, 1, 2, 7, 1, 5, 4, 1, 2, 16, 1, 3, 17, 1, 2, 8, 1, 18, 6, 1, 2, 3, 1, 4, 19, 1, 2, 5, 1, 9, 3, 1, 2, 20, 1, 21, 4, 1, 2, 7, 1, 3, 10, 1, 2, 22, 1, 5, 6, 1, 2, 3, 1, 4, 23, 1

Offset

1,2

Comments

Take the sequence of natural numbers:

s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,

Move the first term s(1)=1 to 2*1 places to the right:

s1=2,3,1,4,5,6,7,8,9,10,11,12,13,14,15,16,

Move the first term s(1)=2 to 2*2 places to the right:

s2=3,1,4,5,2,6,7,8,9,10,11,12,13,14,15,16,

Repeating the procedure we get successively:

s3=1,4,5,2,6,7,3,8,9,10,11,12,13,14,15,16,

s4=4,5,1,2,6,7,3,8,9,10,11,12,13,14,15,16,

s5=5,1,2,6,7,3,8,9,4,10,11,12,13,14,15,16,

s6=1,2,6,7,3,8,9,4,10,11,5,12,13,14,15,16,

.......................................................................

s100=8,3,1,2,24,25,4,5,12,7,6,26,9,27,13,28,29,10,14,30,31,15,11,

32,33,16,34,35,17,36,37,18,38,39,19,40,41,20,42,43,21,44,45,22,

46,47,23,48,49,50,51,52,53,54,55,56,57,58,59,60,

The sequence A104706 gives the first terms in the rearrangements s0,s1,s2,...,s100. Cf. A104705

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A028920(2n-1)-1. - Benoit Cloitre, Mar 09 2007

Maple

A104706:= proc(N) # to produce a(1) .. a(N)
    local A, R, n, M;
    M:= N;
    R:= $1..M;
    A[1]:= 1;
    for n from 2 to N do
       if 2*R[1]+1 > M then
         R:= R, [$M+1..M+N]
       fi;
       R:= R[2..2*R[1]+1], R[1], R[2*R[1]+2..N];
       A[n]:= R[1];
    od:
    seq(A[n], n=1..N);
end proc:
A104706(100); # Robert Israel, Dec 04 2015

Mathematica

s=Range[100]; bb={1}; Do[s=Drop[Insert[s, s[[1]], 2+2s[[1]]], 1]; bb=Append[bb, s[[1]]], {i, 100}]; bb
NestList[Rest[Insert[#, #[[1]], 2 + 2 #[[1]]]] &, Range[30], 30][[All, 1]] (* Birkas Gyorgy, Mar 03 2011 *)

Prog

(Sage)
def A104706(n):
    m, N = 2, 2*n-1
    while true:
        if m.divides(N): return m-2
        N = N*(m-1)//m
        m += 1
print([A104706(n) for n in (1..97)]) # Peter Luschny, Dec 04 2015

Crossrefs

Cf. A104705, A028920.

Sequence in context: A329721 A193790 A055446 * A366796 A094137 A038802

Adjacent sequences: A104703 A104704 A104705 * A104707 A104708 A104709

Keyword

easy,nonn

Author

Zak Seidov, Mar 19 2005

Status

approved