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

1,2

Comments

Take the sequence of natural numbers:

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

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

Links

Table of n, a(n) for n=1..90.

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

Crossrefs

Cf. A104705, A104706.

Sequence in context: A253028 A133108 A055441 * A067003 A277884 A117386

Adjacent sequences: A104714 A104715 A104716 * A104718 A104719 A104720

Keyword

easy,nonn

Author

Zak Seidov, Mar 20 2005

Status

approved