cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A318479 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * (i-1)^k (where i denotes the imaginary unit); a(n) is the square of the modulus of h(n).

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%I A318479 #15 Nov 30 2020 22:37:45
%S A318479 0,1,2,1,4,5,2,1,8,13,10,13,4,9,2,5,16,9,26,17,20,13,26,17,8,5,18,13,
%T A318479 4,1,10,5,32,41,18,25,52,61,34,41,40,53,26,37,52,65,34,45,16,17,10,9,
%U A318479 36,37,26,25,8,13,2,5,20,25,10,13,64,65,82,81,36,37,50
%N A318479 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * (i-1)^k (where i denotes the imaginary unit); a(n) is the square of the modulus of h(n).
%C A318479 See A318438 for the real part of h and additional comments.
%H A318479 Rémy Sigrist, <a href="/A318479/b318479.txt">Table of n, a(n) for n = 0..10000</a>
%H A318479 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A318479 a(n) = A318438(n)^2 + A318439(n)^2.
%F A318479 a(2^k) = 2^k for any k >= 0.
%F A318479 a(3 * 2^k) = 2^k for any l >= 0.
%o A318479 (PARI) a(n) = my (d=Vecrev(digits(n, 2))); norm(sum(i=1, #d, d[i]*(I-1)^(i-1)))
%Y A318479 Cf. A318438, A318439.
%K A318479 nonn,look,base
%O A318479 0,3
%A A318479 _Rémy Sigrist_, Aug 27 2018