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A104717 First terms in the rearrangements of integer numbers (see comments). 3


%S 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,

%T 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,

%U 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

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

%C Take the sequence of natural numbers:

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

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

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

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

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

%C Repeating the procedure we get successively:

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

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

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

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

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

%C ........................................................................

%C 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,

%C 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,

%C 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,

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

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

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

%t 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

%Y Cf. A104705, A104706.

%K easy,nonn

%O 1,2

%A _Zak Seidov_, Mar 20 2005

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Last modified November 30 15:30 EST 2021. Contains 349420 sequences. (Running on oeis4.)