A091230 Iterates of A014580, starting with a(0) = 1, a(n) = A014580^(n)(1). [Here A014580^(n) means the n-th fold application of A014580].

1, 2, 3, 7, 25, 137, 1123, 13103, 204045, 4050293, 99440273

Offset: 0

Author

Antti Karttunen, Jan 03 2004

Keywords

• nonn

Links

• A. Karttunen, Scheme-program for computing this sequence.
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

Cf. A000079, A007097, A091238, A091204-A091205, A245701-A245702, A245703-A245704.

Programs

PARI

isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
prev=1; i=0; print1(1, ", "); for(n=1, 123456789, if(isA014580(n), i++; if((i == prev), print1(n, ", "); prev=n))) \\ Antti Karttunen, Aug 02 2014

Formula

a(0)=1, a(n) = A014580(a(n-1)). [The defining recurrence].

From Antti Karttunen, Aug 03 2014: (Start)

Other identities. For all n >= 0, the following holds:

A091238(a(n)) = n+1.

a(n) = A091204(A007097(n)) and A091205(a(n)) = A007097(n).

a(n) = A245703(A007097(n)) and A245704(a(n)) = A007097(n).

a(n) = A245702(A000079(n)) and A245701(a(n)) = A000079(n).

(End)

Extensions

Terms a(8)-a(10) computed by Antti Karttunen, Aug 02 2014