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

%I A103951 #12 Mar 17 2015 09:32:04
%S A103951 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 A103951 68,72,75,76,79,83,84,87,92,93,96,102,103,105,106,113,114,116,117,125,
%U A103951 126,128,129,137,138,139,142,143,152,153,154,157,158,162,168,169,171
%N A103951 Procedure "Remove every 10th term!" executed 10 times.
%C A103951 Procedure A067251, "Every 10th number has been omitted", executed 10 times.
%C A103951 0. Start with the sequence of natural numbers:
%C A103951 s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
%C A103951 1. Remove each 10th term:
%C A103951 s1=1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,...
%C A103951 2. Remove each 10th term:
%C A103951 s2=1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,21,23,24,...
%C A103951 After 10 executions we have:
%C A103951 s10=1,2,3,4,5,6,7,8,9,21,23,25,27,29,32,35,38,42,46,49,...
%C A103951 This algorithm may be generalized to
%C A103951 "Remove each k-th term k times!". We have then
%C A103951 k=2: s2=1,5,9,13,17,21,25,29,33,37,41,45,... a(n)=4n-3 (n=1,2,...)
%C A103951 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 A103951 k=4: s4=1,2,3, 9,11,14,18,22,23,29,30,33,38,39,43,46,50,51
%C A103951 k=5, s5=1,2,3, 4,11,13,16,19,23,26,28,32,34,39,41,42,48,51,52
%C A103951 k=6, s6=1,2,3, 4, 5,13,15,17,20,23,27,31,32,37,38,44,45,47,52,53
%C A103951 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 A103951 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 A103951 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 A103951 Is there any general rule for a_k(n)?
%H A103951 Harvey P. Dale, <a href="/A103951/b103951.txt">Table of n, a(n) for n = 1..1000</a>
%t A103951 ra=Range[1000];k=10;Do[ra=Drop[ra, {k, Length[ra], k}], {i, k}];ra
%t A103951 Nest[Flatten[Most/@Partition[#,10]]&,Range[300],10] (* _Harvey P. Dale_, Mar 17 2015 *)
%Y A103951 Cf. A067251.
%K A103951 nonn
%O A103951 1,2
%A A103951 _Zak Seidov_, Feb 22 2005