The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A332412 a(n) is the real 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 A332413 gives imaginary parts. 3
 0, 1, 0, -1, 0, 3, 4, 3, 2, 3, 0, 1, 0, -1, 0, -3, -2, -3, -4, -3, 0, 1, 0, -1, 0, 9, 10, 9, 8, 9, 12, 13, 12, 11, 12, 9, 10, 9, 8, 9, 6, 7, 6, 5, 6, 9, 10, 9, 8, 9, 0, 1, 0, -1, 0, 3, 4, 3, 2, 3, 0, 1, 0, -1, 0, -3, -2, -3, -4, -3, 0, 1, 0, -1, 0, -9, -8, -9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The representation of {f(n)} corresponds to the cross form of the Vicsek fractal. As a set, {f(n)} corresponds to the Gaussian integers whose real and imaginary parts have not simultaneously a nonzero digit at the same place in their balanced ternary representations. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..15624 Rémy Sigrist, Colored representation of f(n) for n = 0..5^6-1 in the complex plan (where the hue is function of n) Wikipedia, Vicsek fractal FORMULA a(n) = 0 iff the n-th row of A031219 has only even terms. a(5*n)   = 3*a(n). a(5*n+1) = 3*a(n) + 1. a(5*n+2) = 3*a(n). a(5*n+3) = 3*a(n) - 1. a(5*n+4) = 3*a(n). 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) = -1. PROG (PARI) a(n) = { my (d=Vecrev(digits(n, 5))); real(sum (k=1, #d, if (d[k], 3^(k-1)*I^(d[k]-1), 0))) } CROSSREFS See A332497 for a similar sequence. Cf. A031219, A289813, A332413 (imaginary parts). Sequence in context: A308430 A280136 A258451 * A333229 A164358 A275638 Adjacent sequences:  A332409 A332410 A332411 * A332413 A332414 A332415 KEYWORD sign,base AUTHOR Rémy Sigrist, Feb 12 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 10 14:10 EDT 2020. Contains 335576 sequences. (Running on oeis4.)