A343275 a(n) = |2*n - 10^length(n)|.

8, 6, 4, 2, 0, 2, 4, 6, 8, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40

Offset

1,1

Comments

The plot looks like multiple V shapes. A new V shape occurs for each interval n = 10^k .. 10^(k+1)-1, with the bottom of the V at a(5*10^k) = 0.

All terms are even.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..9999

Erhan Tezcan, Github Repo includes plots and the code.

Formula

a(n) = abs(2*n - 10^A055642(n)).

a(10*n) = 10*a(n).

Example

n=10 has length 2, so a(10) = |20-100| = 80.

Mathematica

Table[Abs[2n-10^IntegerLength[n]], {n, 70}] (* Harvey P. Dale, Dec 11 2022 *)

Prog

(Python)
def a(n : int) -> int:
  return abs((n << 1) - (10 ** len(str(n))))
(PARI) a(n) = abs(2*n-10^max(1, #digits(n))) \\ Rémy Sigrist, May 30 2021

Crossrefs

Cf. A055642.

Sequence in context: A263181 A298978 A199151 * A177154 A059631 A333198

Adjacent sequences: A343272 A343273 A343274 * A343276 A343277 A343278

Keyword

nonn,base

Author

Erhan Tezcan, Apr 10 2021

Status

approved