A280506 Nonpalindromic part of n in base 2 (with carryless GF(2)[X] factorization): a(n) = A280500(n,A280505(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 13, 1, 1, 1, 1, 1, 19, 1, 1, 11, 13, 1, 25, 13, 1, 1, 11, 1, 1, 1, 1, 1, 13, 1, 37, 19, 11, 1, 41, 1, 25, 11, 1, 13, 47, 1, 11, 25, 1, 13, 19, 1, 55, 1, 13, 11, 59, 1, 61, 1, 1, 1, 1, 1, 67, 1, 69, 13, 61, 1, 1, 37, 13, 19, 59, 11, 25, 1, 81, 41, 11, 1, 1, 25, 87, 11, 55, 1, 91, 13, 1, 47, 19, 1, 97, 11, 1, 25, 13, 1, 103

Offset: 1

Author

Antti Karttunen, Jan 09 2017

Keywords

• nonn
• base

Comments

a(n) = number obtained when the maximal base-2 palindromic divisor of n, A280505(n), is divided out of n with carryless GF(2)[X] factorization (see examples of A280500 for the explanation).

Apart from 1, all terms are present in A164861 (form their proper subset).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences related to binary expansion of n
• Index entries for sequences operating on polynomials in ring GF(2)[X]

Crossrefs

Cf. A000265, A048720, A057889, A057891, A164861, A280500, A280502, A280504, A280508, A280509.

Cf. A057890 (positions of ones).

Programs

Scheme

(define (A280506 n) (A280500bi n (A280505 n))) ;; Code for A280500bi given in A280500.

Formula

a(n) = A280500(n,A280505(n)).

Other identities. For all n >= 1:

a(2n) = a(A000265(n)) = a(n).

A048720(a(n), A280505(n)) = n.

Extensions

Erroneous claim removed from comments by Antti Karttunen, May 13 2018