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Difference between value of n, when remultiplied "upward", from GF(2)[X] to N, and when remultiplied "downward", from N to GF(2)[X]: a(n) = A234742(n) - A234741(n).
7

%I #12 Aug 11 2015 01:23:51

%S 0,0,0,0,0,4,0,0,0,16,8,0,0,0,0,12,0,64,32,0,16,40,0,16,0,8,0,48,0,4,

%T 24,0,0,64,128,64,64,0,0,76,32,0,80,32,0,172,32,0,0,56,16,192,0,4,96,

%U 16,0,64,8,0,48,0,0,120,0,384,128,0,256,64,128,112,128,0,0,300,0,128,152,96,64,152,0,148,160,644,64

%N Difference between value of n, when remultiplied "upward", from GF(2)[X] to N, and when remultiplied "downward", from N to GF(2)[X]: a(n) = A234742(n) - A234741(n).

%C All terms are divisible by 4.

%C a(n) = 0 iff both A236378(n) and A236379(n) are zero, or in other words, iff A234741(n)=n and A234742(n)=n, which means that A235032 gives all such n, that a(n) = 0.

%H Antti Karttunen, <a href="/A236380/b236380.txt">Table of n, a(n) for n = 0..8191</a>

%F a(n) = A234742(n) - A234741(n).

%F a(n) = A236378(n) + A236379(n).

%o (Scheme, two variants)

%o (define (A236380 n) (- (A234742 n) (A234741 n)))

%o (define (A236380v2 n) (+ (A236378 n) (A236379 n)))

%Y A235032 gives the positions of zeros, A235033 the positions of nonzeros.

%Y Cf. also A234741, A234742, A236378, A236379, A236851, A061858.

%K nonn

%O 0,6

%A _Antti Karttunen_, Jan 24 2014