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

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

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