1,1

Let f(n) denote the n-th term of the current working sequence. Start with the natural integers:

1,2,3,4,5,6,7,8,9,10,11,12,...

Delete the term in position f(1), which is f(f(1))=f(1)=1, leaving:

2,3,4,5,6,7,8,9,10,11,12,...

Delete the term in position f(2), which is f(f(2))=f(3)=4, leaving:

2,3,5,6,7,8,9,10,11,12,...

Delete the term in position f(3), which is f(f(3))=f(5)=7, leaving:

2,3,5,6,8,9,10,11,12,...

Delete the term in position f(4), which is f(f(4))=f(6)=9, leaving:

2,3,5,6,8,10,11,12,...

Iterating the "sieve" indefinitely produces the sequence:

2,3,5,6,8,10,11,13,14,16,18,19,21,23,24,26,27,29,31,32,34,35,37,39,...

Index entries for sequences generated by sieves

a(n) = floor(n*phi+2-phi) where phi=(1+sqrt(5))/2. Also a(a(...a(1)...)) with n iterations equals F(n+1)=A000045(n+1).

For n>0 and k>0 we have a(a(n)+F(k)-(1+(-1)^k)/2) = a(a(n))+F(k+1)-1-(-1)^k - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 22 2004

Numbers n such that a(n+1)-a(n)=2 are given by A004956.

If prefixed by an initial 1, same as A026355.

Cf. A136119.

Complement of A007066 [From Gerald Hillier (adr.rabbicat(AT)gmail.com), Dec 19 2008]

Sequence in context: A047448 A029921 A026355 this_sequence A007067 A092979 A135260

Adjacent sequences: A099264 A099265 A099266 this_sequence A099268 A099269 A099270

nonn,easy,nice

Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 15 2002