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A103951 Procedure "Remove every 10th term!" executed 10 times. 1


%S 1,2,3,4,5,6,7,8,9,21,23,25,27,29,32,35,38,42,46,49,51,54,56,59,62,65,

%T 68,72,75,76,79,83,84,87,92,93,96,102,103,105,106,113,114,116,117,125,

%U 126,128,129,137,138,139,142,143,152,153,154,157,158,162,168,169,171

%N Procedure "Remove every 10th term!" executed 10 times.

%C Procedure A067251, "Every 10th number has been omitted", executed 10 times.

%C 0. Start with 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 1. Remove each 10th term:

%C s1=1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,...

%C 2. Remove each 10th term:

%C s2=1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,21,23,24,...

%C After 10 executions we have:

%C s10=1,2,3,4,5,6,7,8,9,21,23,25,27,29,32,35,38,42,46,49,...

%C This algorithm may be generalized to

%C "Remove each k-th term k times!". We have then

%C k=2: s2=1,5,9,13,17,21,25,29,33,37,41,45,... a(n)=4n-3 (n=1,2,...)

%C k=3: s3=1,2,7,10,14,16,20,23,28,29,34,37,41,43,47,50,55, (no simple rule here and further?)

%C k=4: s4=1,2,3, 9,11,14,18,22,23,29,30,33,38,39,43,46,50,51

%C k=5, s5=1,2,3, 4,11,13,16,19,23,26,28,32,34,39,41,42,48,51,52

%C k=6, s6=1,2,3, 4, 5,13,15,17,20,23,27,31,32,37,38,44,45,47,52,53

%C k=7, s7=1,2,3, 4, 5, 6,15,17,19,22,25,29,33,34,38,39,44,45,51,52,54

%C k=8, s8=1,2,3, 4, 5, 6, 7,17,19,21,23,26,29,33,37,39,42,44,47,50,53

%C k=9, s9=1,2,3, 4, 5, 6, 7, 8,19,21,23,25,28,31,34,38,42,43,47,48,52,

%C Is there any general rule for a_k(n)?

%H Harvey P. Dale, <a href="/A103951/b103951.txt">Table of n, a(n) for n = 1..1000</a>

%t ra=Range[1000];k=10;Do[ra=Drop[ra, {k, Length[ra], k}], {i, k}];ra

%t Nest[Flatten[Most/@Partition[#,10]]&,Range[300],10] (* _Harvey P. Dale_, Mar 17 2015 *)

%Y Cf. A067251.

%K nonn

%O 1,2

%A _Zak Seidov_, Feb 22 2005

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