A280501 "Blue kernel" of n: a(n) = A091255(n, A193231(n)).

1, 1, 1, 1, 1, 6, 7, 1, 7, 6, 1, 6, 1, 7, 1, 1, 1, 18, 19, 20, 21, 1, 1, 6, 1, 1, 7, 7, 1, 6, 1, 1, 1, 6, 7, 18, 1, 19, 1, 20, 1, 21, 1, 1, 7, 6, 1, 6, 7, 1, 1, 1, 19, 18, 1, 7, 1, 6, 1, 20, 1, 1, 21, 1, 21, 6, 1, 20, 1, 7, 1, 18, 1, 1, 1, 19, 1, 6, 7, 20, 1, 1, 7, 21, 1, 6, 1, 1, 1, 18, 1, 6, 7, 1, 19, 6, 1, 7, 1, 1, 7, 6, 1, 1, 1, 106, 107, 108, 109, 1, 1, 7

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences related to binary expansion of n

Index entries for sequences operating on polynomials in ring GF(2)[X]

Formula

a(n) = A091255(n, A193231(n)).

Other identities. For all n >= 1:

a(A193231(n)) = a(n).

A048720(a(n), A280502(n)) = n.

Prog

(Scheme) (define (A280501 n) (A091255bi n (A193231 n))) ;; A091255bi implements the 2-argument GF(2)[X] GCD-function (A091255).
(PARI)
A091255sq(a, b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2), Pol(binary(b))*Mod(1, 2)))), 2);
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ From A193231
A280501(n) = A091255sq(n, A193231(n)); \\ Antti Karttunen, Jan 12 2020

Crossrefs

Cf. A048720, A091255, A193231, A280502, A280505, A331167.

Sequence in context: A294644 A256128 A373020 * A244818 A244682 A201323

Adjacent sequences: A280498 A280499 A280500 * A280502 A280503 A280504

Keyword

nonn,look,base

Author

Antti Karttunen, Jan 09 2017

Status

approved