A104717 First terms in the rearrangements of integer numbers (see comments).

1, 2, 3, 4, 1, 5, 6, 7, 1, 2, 8, 9, 1, 10, 3, 11, 1, 2, 12, 13, 1, 4, 14, 15, 1, 2, 16, 3, 1, 5, 17, 18, 1, 2, 19, 6, 1, 20, 4, 3, 1, 2, 21, 22, 1, 7, 23, 24, 1, 2, 25, 5, 1, 3, 8, 26, 1, 2, 4, 27, 1, 28, 9, 29, 1, 2, 3, 6, 1, 30, 31, 10, 1, 2, 32, 4, 1, 5, 3, 33, 1, 2, 34, 7, 1, 11, 35, 36, 1, 2

Offset: 1

Author

Zak Seidov, Mar 20 2005

Keywords

• easy
• nonn

Comments

Take the sequence of natural numbers:

s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,

Move the first term s(1)=1 to 3*1=3 places to the right:

s1=2,3,4,1,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,

Move the first term s(1)=2 to 3*2=6 places to the right:

s2={3,4,1,5,6,7,2,8,9,10,11,12,13,14,15,16,17,18,19,20,

Repeating the procedure we get successively:

s3={4,1,5,6,7,2,8,9,10,3,11,12,13,14,15,16,17,18,19,20,

s4={1,5,6,7,2,8,9,10,3,11,12,13,4,14,15,16,17,18,19,20,

s5={5,6,7,1,2,8,9,10,3,11,12,13,4,14,15,16,17,18,19,20,

s6={6,7,1,2,8,9,10,3,11,12,13,4,14,15,16,5,17,18,19,20,

s7={7,1,2,8,9,10,3,11,12,13,4,14,15,16,5,17,18,19,6,20,

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

s100=1,5,39,3,2,40,13,41,42,4,43,9,14,7,44,45,46,6,15,47,10,48,49,16,8,50,

51,52,11,17,53,54,55,18,56,12,57,58,19,59,60,61,20,62,63,64,21,65,66,67,22,

68,69,70,23,71,72,73,24,74,75,76,25,77,78,79,26,80,81,82,27,83,84,85,28,86,

87,88,29,89,90,91,30,92,93,94,31,95,96,97,32,98,99,100,33,101,102,103,34,

104,105,106,35,107,108,109,36,110,111,112,37,113,114,115,38,116,117,

The sequence A104717 gives the first terms in the rearrangements s0,s1,s2,...,s100. Cf. A104705, A104706

Crossrefs

Cf. A104705, A104706.

Programs

Mathematica

s=Range[200];bb={1};Do[s=Drop[Insert[s, s[[1]], 2+3 s[[1]]], 1];bb=Append[bb, s[[1]]], {i, 100}];bb