A332550 The 10-block imbalance of n (see Comments for definition).

9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 17

Offset

0,1

Comments

In a certain country, digits come in sealed boxes containing 10 distinct digits each. To write the number 2019 you can open a single box and extract the digits 2, 0, 1, and 9.

We call the "imbalance" of 2019 the number of unused digit in the opened box(es). So writing 2019 leaves an imbalance of 6 (the 6 unused digits in the box).

If we want to write 2020 we must open two boxes - and leave behind 8 digits in the first box and 8 digits in the second one. This produces for 2020 an imbalance of 16.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Eric Angelini, Integer + imbalance, Feb 20 2020.

Example

10 has an imbalance of 8 - there are two unused digits in the box. For 11 we have to open two boxes to get the two 1's, leaving an imbalance of 9+9 = 18.

Mathematica

Array[10*Max@ #2[[All, -1]] - Length@ #1 & @@ {#, Tally@ #} &@ IntegerDigits@ # &, 101, 0] (* Michael De Vlieger, Feb 21 2020 *)

Crossrefs

Cf. A332551.

Sequence in context: A116667 A259151 A270172 * A137577 A363118 A363019

Adjacent sequences: A332547 A332548 A332549 * A332551 A332552 A332553

Keyword

nonn,base

Author

N. J. A. Sloane, Feb 21 2020, based on a message from Eric Angelini, Feb 20 2020

Status

approved