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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 09 2017

Keywords

• nonn
• base

Comments

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.

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.

All terms are in A057890 and each term of A057890 occurs an infinite number of times.

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. A048720, A057889, A057890, A091222, A091255, A280501, A280503, A280506.

Programs

Scheme

(define (A280505 n) (A091255bi n (A057889 n))) ;; A091255bi implements the 2-argument GF(2)[X] GCD-function (A091255).

Formula

a(n) = A091255(n,A057889(n)).

Other identities. For all n >= 1:

a(A057889(n)) = a(n).

A048720(a(n), A280506(n)) = n.