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A103951 Procedure "Remove every 10th term!" executed 10 times. 1
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, 68, 72, 75, 76, 79, 83, 84, 87, 92, 93, 96, 102, 103, 105, 106, 113, 114, 116, 117, 125, 126, 128, 129, 137, 138, 139, 142, 143, 152, 153, 154, 157, 158, 162, 168, 169, 171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

0. Start with 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,...

1. Remove each 10th term:

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

2. Remove each 10th term:

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

After 10 executions we have:

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

This algorithm may be generalized to

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

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

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?)

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

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

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

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

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

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

Is there any general rule for a_k(n)?

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

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

Nest[Flatten[Most/@Partition[#, 10]]&, Range[300], 10] (* Harvey P. Dale, Mar 17 2015 *)

CROSSREFS

Cf. A067251.

Sequence in context: A082323 A069571 A039173 * A342304 A098951 A097962

Adjacent sequences:  A103948 A103949 A103950 * A103952 A103953 A103954

KEYWORD

nonn

AUTHOR

Zak Seidov, Feb 22 2005

STATUS

approved

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Last modified April 15 10:48 EDT 2021. Contains 342977 sequences. (Running on oeis4.)