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A332413
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a(n) is the imaginary part of f(n) = Sum_{d_k > 0} 3^k * i^(d_k-1) where Sum_{k >= 0} 5^k * d_k is the base 5 representation of n and i denotes the imaginary unit. Sequence A332412 gives real parts.
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2
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0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 3, 3, 4, 3, 2, 0, 0, 1, 0, -1, -3, -3, -2, -3, -4, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 3, 3, 4, 3, 2, 0, 0, 1, 0, -1, -3, -3, -2, -3, -4, 9, 9, 10, 9, 8, 9, 9, 10, 9, 8, 12, 12, 13, 12, 11, 9, 9, 10, 9, 8, 6, 6, 7, 6, 5, 0, 0, 1, 0
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OFFSET
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0,11
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LINKS
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FORMULA
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a(n) = 0 iff the n-th row of A031219 has neither 2's nor 4's.
a(5*n) = 3*a(n).
a(5*n+1) = 3*a(n).
a(5*n+2) = 3*a(n) + 1.
a(5*n+3) = 3*a(n).
a(5*n+4) = 3*a(n) - 1.
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EXAMPLE
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For n = 103:
- 103 = 4*5^2 + 3*5^0,
- so f(123) = 3^2 * i^(4-1) + 3^0 * i^(3-1) = -1 - 9*i,
- and a(n) = -9.
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PROG
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(PARI) a(n) = { my (d=Vecrev(digits(n, 5))); imag(sum (k=1, #d, if (d[k], 3^(k-1)*I^(d[k]-1), 0))) }
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CROSSREFS
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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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