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URL: https://oeis.org/A318704

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A318704
For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the square of the modulus of f(n).
2
0, 1, 1, 2, 4, 1, 5, 2, 4, 5, 1, 2, 8, 5, 5, 2, 16, 25, 17, 26, 4, 9, 5, 10, 20, 29, 17, 26, 8, 13, 5, 10, 16, 17, 25, 26, 20, 17, 29, 26, 4, 5, 9, 10, 8, 5, 13, 10, 32, 41, 41, 50, 20, 25, 29, 34, 20, 29, 25, 34, 8, 13, 13, 18, 64, 49, 65, 50, 100, 81, 101
OFFSET
0,4
COMMENTS
See A318702 for the real part of f and additional comments.
FORMULA
a(n) = A318702(n)^2 + A318703(n)^2.
a(4 * k) = 4 * a(k) for any k >= 0.
PROG
(PARI) a(n) = my (b=Vecrev(binary(n))); norm(sum(k=1, #b, b[k] * I^(k-1) * 2^floor((k-1)/2)))
CROSSREFS
Cf. A318702.
Sequence in context: A077623 A132042 A060370 * A303977 A165064 A299918
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Sep 01 2018
STATUS
approved