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

Author

Zak Seidov, Mar 19 2005

Keywords

• easy
• nonn

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.

Programs

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