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A104706 First terms in the rearrangements of integer numbers (see comments). 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A329721 A193790 A055446 * A366796 A094137 A038802
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Mar 19 2005
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)