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.

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

Offset

0,11

Links

Rémy Sigrist, Table of n, a(n) for n = 0..15624

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

Adjacent sequences: A332410 A332411 A332412 * A332414 A332415 A332416

Keyword

sign,base

Author

Rémy Sigrist, Feb 12 2020

Status

approved