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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).
2
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, 17, 20, 25, 32, 25, 20, 17, 10, 10, 13, 8, 9, 16, 17, 20, 25, 18, 13, 10, 5, 32, 41, 34, 25, 34, 41, 50, 61, 52, 45, 40, 29, 29, 40, 45, 20, 17, 26, 37, 50, 53, 58
OFFSET
0,2
COMMENTS
See A318722 for the real part of g and additional comments.
LINKS
FORMULA
a(n) = A318722(n)^2 + A318723(n)^2.
If A048647(A042968(m)) = A042968(n), then a(m) = a(n).
PROG
(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)
CROSSREFS
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Sep 02 2018
STATUS
approved