A305892 - OEIS

%I #8 Jun 16 2018 18:30:51

%S 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,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,

%U 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1

%N a(n) = 1 if n is composite and the n-th Stern polynomial B(n,x) is irreducible, 0 otherwise.

%C Characteristic function for A186892, apart from its initial term.

%C See also A186891 about related Ulas & Ulas conjecture.

%H Antti Karttunen, <a href="/A305892/b305892.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = (1-A010051(n))*A283991(n).

%o (PARI)

%o ps(n)=if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));

%o A305892(n) = (!isprime(n) && polisirreducible(ps(n))); \\ _Antti Karttunen_, Jun 16 2018, after _Charles R Greathouse IV_'s Apr 07 2015 code for A186892.

%Y Cf. A010051, A186891, A186892, A283991, A284011.

%Y Differs from A305821 for the first time at n=65, where a(65) = 1, while A305821(65) = 0.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 16 2018