A108696 Generated by a sieve: see comments.

1, 2, 3, 5, 7, 11, 13, 19, 23, 31, 35, 43, 49, 59, 61, 79, 83, 103, 109, 119, 133, 151, 155, 175, 193, 211, 215, 241, 259, 275, 283, 323, 331, 361, 373, 403, 419, 443, 455, 499, 511, 541, 571, 613, 623, 649, 673, 719, 733, 781, 803, 841, 871, 919

Offset: 1

Author

David Applegate, Oct 11 2007

Keywords

• nonn

Comments

Start with the natural numbers:

1 2 3 4 5 6 7 8 9 10 11 ...

Accept the 2nd number, 2 and erase every 2nd number after it, giving:

1 2 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 ...

Accept the 3rd number, 3 and erase every 3rd number after it, giving:

1 2 3 5 7 11 13 17 19 23 25 29 31 35 ...

Accept the 4th number, 5 and erase every 4th number after it, giving:

1 2 3 5 7 11 13 19 23 25 31 35 ...

Repeat!

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves

Crossrefs

Equals A007952 + 2 or equally A002491(n) + 1.

Programs

Haskell

a108696 n = a108696_list !! (n-1)
a108696_list = 1 : sieve' 2 [2..] where
   sieve' n (x:xs) = x : (sieve' (n+1) $ sieving xs) where
      sieving xs = (take (n-1) xs) ++ (sieving $ drop n xs)
-- Reinhard Zumkeller, Jul 04 2011

Tcl

source /tclutils/utils.tcl
set l [range 0 10000]; set z z
for {set i 2} {$i*2 <= [llength $l]} {incr i} {
set k [expr {[llength $l]-1}]
set k [expr {$k - ($k % $i)}]
while {$k > $i} {
set l [lreplace $l $k $k]
incr k -$i
}
puts "after $i: length [llength $l], prefix [join [lrange $l 0 10] { }]"
}