A104705 First terms in the rearrangements of integer numbers (see comments).

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

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 prime[s(1)]=2 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 prime[s(1)]=3 places to the right:

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

Repeating the procedure we get successively:

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

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

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

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

s7=5,6,1,2,3,7,8,4,9,10,11,12,13,15,16,

s8=6,1,2,3,7,8,4,9,10,11,12,5,13,15,16,

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

s100=2,3,1,24,9,4,25,26,27,6,5,7,28,29,30,10,8,31,32,11,33,34,35,36,

37,38,12,39,40,41,42,13,43,44,14,45,46,47,48,15,49,50,51,52,53,54,

16,55,56,57,58,59,60,17,61,62,18,63,64,65,66,67,68,19,69,70,71,72,

20,73,74,21,75,76,77,78,79,80,22,81,82,83,84,23,85,86,87,88,89,90,

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

Links

Table of n, a(n) for n=1..99.

Mathematica

s=Range[100]; bb={1}; Do[s=Drop[Insert[s, s[[1]], 2+Prime[s[[1]]]], 1]; bb=Append[bb, s[[1]]], {i, 100}]; bb

Crossrefs

Sequence in context: A336811 A255250 A273620 * A143361 A152547 A083906

Adjacent sequences: A104702 A104703 A104704 * A104706 A104707 A104708

Keyword

easy,nonn

Author

Zak Seidov, Mar 19 2005

Status

approved