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A332413 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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,11
LINKS
FORMULA
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.
EXAMPLE
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.
PROG
(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))) }
CROSSREFS
Cf. A031219, A289814, A332412 (real parts and additional comments).
Sequence in context: A082924 A159636 A023647 * A239207 A329157 A082978
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Feb 12 2020
STATUS
approved

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)