cp's OEIS Frontend

A318724 Let f(0) = 0 and f(t*4^k + u) = i^t * ((1+i) * 2^k - f(u)) for any t in {1, 2, 3} and k >= 0 and u such that 0 <= u < 4^k (i denoting the imaginary unit); for any n >= 0, let g(n) = (f(A042968(n)) - 1 - i) / 2; a(n) is the square of the modulus of g(n).

%I A318724 #13 Sep 04 2018 03:06:05
%S A318724 1,2,1,2,5,4,5,8,5,4,5,2,8,13,10,5,10,13,18,25,20,17,16,9,13,18,13,10,
%T A318724 17,20,25,32,25,20,17,10,10,13,8,9,16,17,20,25,18,13,10,5,32,41,34,25,
%U A318724 34,41,50,61,52,45,40,29,29,40,45,20,17,26,37,50,53,58
%N A318724 Let f(0) = 0 and f(t*4^k + u) = i^t * ((1+i) * 2^k - f(u)) for any t in {1, 2, 3} and k >= 0 and u such that 0 <= u < 4^k (i denoting the imaginary unit); for any n >= 0, let g(n) = (f(A042968(n)) - 1 - i) / 2; a(n) is the square of the modulus of g(n).
%C A318724 See A318722 for the real part of g and additional comments.
%H A318724 Rémy Sigrist, <a href="/A318724/b318724.txt">Table of n, a(n) for n = 0..12287</a>
%F A318724 a(n) = A318722(n)^2 + A318723(n)^2.
%F A318724 If A048647(A042968(m)) = A042968(n), then a(m) = a(n).
%o A318724 (PARI) a(n) = my (d=Vecrev(digits(1+n+n\3,4)), z=0); for (k=1, #d, if (d[k], z = I^d[k] * (-z + (1+I) * 2^(k-1)))); norm((z-1-I)/2)
%Y A318724 Cf. A042968, A048647, A318722, A318723.
%K A318724 nonn,base,look
%O A318724 0,2
%A A318724 _Rémy Sigrist_, Sep 02 2018