cp's OEIS Frontend

A280505 The palindromic kernel of n in base 2 (with carryless GF(2)[X] factorization): a(n) = A091255(n,A057889(n)).

%I A280505 #19 Jan 10 2017 19:14:22
%S A280505 1,2,3,4,5,6,7,8,9,10,1,12,1,14,15,16,17,18,1,20,21,2,3,24,1,2,27,28,
%T A280505 3,30,31,32,33,34,7,36,1,2,5,40,1,42,3,4,45,6,1,48,7,2,51,4,3,54,1,56,
%U A280505 5,6,1,60,1,62,63,64,65,66,1,68,1,14,3,72,73,2,15,4,3,10,7,80,1,2,9,84,85,6,1,8,3,90,1,12,93,2,5,96,1,14,99,4,9,102,1,8,15,6
%N A280505 The palindromic kernel of n in base 2 (with carryless GF(2)[X] factorization): a(n) = A091255(n,A057889(n)).
%C A280505 a(n) = the maximal GF(2)[X]-divisor of n which in base 2 is either a palindrome or becomes a palindrome if trailing 0's are omitted.
%C A280505 More precisely: a(n) = the unique term m of A057890 for which A280500(n,m) > 0 and A091222(m) >= A091222(k) for all such terms k of A057890 for which A280500(n,k) > 0.
%C A280505 All terms are in A057890 and each term of A057890 occurs an infinite number of times.
%H A280505 Antti Karttunen, <a href="/A280505/b280505.txt">Table of n, a(n) for n = 1..8192</a>
%H A280505 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A280505 <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>
%F A280505 a(n) = A091255(n,A057889(n)).
%F A280505 Other identities. For all n >= 1:
%F A280505 a(A057889(n)) = a(n).
%F A280505 A048720(a(n), A280506(n)) = n.
%o A280505 (Scheme) (define (A280505 n) (A091255bi n (A057889 n))) ;; A091255bi implements the 2-argument GF(2)[X] GCD-function (A091255).
%Y A280505 Cf. A048720, A057889, A057890, A091222, A091255, A280501, A280503, A280506.
%K A280505 nonn,base
%O A280505 1,2
%A A280505 _Antti Karttunen_, Jan 09 2017