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A348653
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For any nonnegative number n with base-13 expansion Sum_{k >= 0} d_k*13^k, a(n) is the imaginary part of Sum_{k >= 0} g(d_k)*(3+2*i)^k where g(0) = 0, and g(1+u+3*v) = (1+u*i)*i^v for any u = 0..2 and v = 0..3 (where i denotes the imaginary unit); see A348652 for the real part.
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3
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0, 0, 1, 2, 1, 1, 1, 0, -1, -2, -1, -1, -1, 2, 2, 3, 4, 3, 3, 3, 2, 1, 0, 1, 1, 1, 5, 5, 6, 7, 6, 6, 6, 5, 4, 3, 4, 4, 4, 8, 8, 9, 10, 9, 9, 9, 8, 7, 6, 7, 7, 7, 3, 3, 4, 5, 4, 4, 4, 3, 2, 1, 2, 2, 2, 1, 1, 2, 3, 2, 2, 2, 1, 0, -1, 0, 0, 0, -1, -1, 0, 1, 0, 0
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OFFSET
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0,4
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COMMENTS
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The function f defines a bijection from the nonnegative integers to the Gaussian integers.
The following diagram depicts g(d) for d = 0..12:
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+ + + +
6 5 |4 2
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--------+----+----+-------
7 |0 1
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+ + + +
8 |10 11 12
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9 |
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LINKS
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FORMULA
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PROG
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(PARI) g(d) = { if (d==0, 0, (1+I*((d-1)%3))*I^((d-1)\3)) }
a(n) = imag(subst(Pol([g(d)|d<-digits(n, 13)]), 'x, 3+2*I))
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CROSSREFS
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See A316658 for a similar sequence.
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KEYWORD
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sign,base
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AUTHOR
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STATUS
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approved
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