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

1,2

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

Prog

(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] { }]"
}
(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

Crossrefs

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

Sequence in context: A233893 A232824 A078334 * A215642 A092581 A362527

Adjacent sequences: A108693 A108694 A108695 * A108697 A108698 A108699

Keyword

nonn

Author

David Applegate, Oct 11 2007

Status

approved