A280501 - OEIS

%I #13 Jan 12 2020 23:49:50

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A280501/b280501.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A280501/a280501.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>

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

%F Other identities. For all n >= 1:

%F a(A193231(n)) = a(n).

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

%o (Scheme) (define (A280501 n) (A091255bi n (A193231 n))) ;; A091255bi implements the 2-argument GF(2)[X] GCD-function (A091255).

%o (PARI)

%o A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);

%o A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ From A193231

%o A280501(n) = A091255sq(n, A193231(n)); \\ _Antti Karttunen_, Jan 12 2020

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

%K nonn,look,base

%O 1,6

%A _Antti Karttunen_, Jan 09 2017