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A280506
Nonpalindromic part of n in base 2 (with carryless GF(2)[X] factorization): a(n) = A280500(n,A280505(n)).
8
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
1,11
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).
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.
PROG
(Scheme) (define (A280506 n) (A280500bi n (A280505 n))) ;; Code for A280500bi given in A280500.
CROSSREFS
Cf. A057890 (positions of ones).
Sequence in context: A282219 A279247 A281096 * A222803 A201132 A212488
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jan 09 2017
EXTENSIONS
Erroneous claim removed from comments by Antti Karttunen, May 13 2018
STATUS
approved