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A280501
"Blue kernel" of n: a(n) = A091255(n, A193231(n)).
6
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
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
KEYWORD
nonn,look,base
AUTHOR
Antti Karttunen, Jan 09 2017
STATUS
approved