OFFSET
1,3
LINKS
Eric Angelini, Balanced numbers, personal blog, May 2024.
Hans Havermann, 10000-term b-file.
EXAMPLE
We place the k digits of a number in succession in k adjacent square boxes forming a rectangle of base k and height 1. We can only place a vertical blade under this rectangle in two ways: exactly between two boxes [positions (a) and (d) below)] or exactly under the middle of a box [position (b) and (c) below)].
If the blade is placed in position (a) between the two 1s of 11, the number 11 is stable.
If the blade is placed in (b) exactly under the 0 of 101, the number 101 is stable.
If the blade is placed in (c) exactly under the 1 of 10, the number is stable.
If the blade is placed in (d) between the 0 and the 2 of 102, the number 102 is stable.
For the last two examples, the balance of the number considered can be explained as follows: the distance which separates a digit from the blade comes into play - the more this distance increases, the heavier the digit in question is. So, the digit 1 of 102 weighs 2 in reality (weight*distance = 1*2 = 2). This quantity balances the influence of the 2 of 102 (for which weight*distance = 2*1 = 2 too).
.
.+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
.| | | | | | | | | | | | | | | |
.+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
.| | 1 | 1 | | 1 | 0 | 1 | | 1 | 0 | | 1 | 0 | 2 | |
.+---+---a---+---+---+-b-+---+---+-c-+---+---+---+---d---+---+
.| | | | | | | | | | | | | | | |
.+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Giorgos Kalogeropoulos, May 25 2024
STATUS
approved