cp's OEIS Frontend

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

%I A280501 #13 Jan 12 2020 23:49:50
%S A280501 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 A280501 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 A280501 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 A280501 "Blue kernel" of n: a(n) = A091255(n, A193231(n)).
%H A280501 Antti Karttunen, <a href="/A280501/b280501.txt">Table of n, a(n) for n = 1..16384</a>
%H A280501 Antti Karttunen, <a href="/A280501/a280501.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A280501 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A280501 <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>
%F A280501 a(n) = A091255(n, A193231(n)).
%F A280501 Other identities. For all n >= 1:
%F A280501 a(A193231(n)) = a(n).
%F A280501 A048720(a(n), A280502(n)) = n.
%o A280501 (Scheme) (define (A280501 n) (A091255bi n (A193231 n))) ;; A091255bi implements the 2-argument GF(2)[X] GCD-function (A091255).
%o A280501 (PARI)
%o A280501 A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
%o A280501 A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ From A193231
%o A280501 A280501(n) = A091255sq(n, A193231(n)); \\ _Antti Karttunen_, Jan 12 2020
%Y A280501 Cf. A048720, A091255, A193231, A280502, A280505, A331167.
%K A280501 nonn,look,base
%O A280501 1,6
%A A280501 _Antti Karttunen_, Jan 09 2017