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A305821
a(n) = 1 if n is composite and its binary expansion encodes an irreducible (0,1)-polynomial when factored over Q, 0 otherwise.
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1
OFFSET
1
COMMENTS
Characteristic function for A206075, apart from its initial term.
FORMULA
a(n) = A257000(n) - A010051(n).
EXAMPLE
For n = 25 we know that it is composite as 25 = 5*5, but nevertheless, its binary representation "11001" encodes a (0,1)-polynomial x^4 + x^3 + 1, which is irreducible when factored over Q, thus a(25) = 1.
PROG
(PARI) A305821(n) = (!isprime(n) && polisirreducible(Pol(binary(n))));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 10 2018
STATUS
approved