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A373117
Stable numbers on vertical blade (see the Example section for an explanation).
0
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 102, 110, 111, 113, 121, 124, 131, 135, 141, 146, 151, 157, 161, 168, 171, 179, 181, 191, 200, 201, 202, 204, 212, 215, 220, 222, 226, 232, 237, 242, 248, 252, 259, 262, 272, 282, 292, 300, 303, 306, 311
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
Sequence in context: A190220 A113586 A061362 * A096091 A084050 A281625
KEYWORD
base,nonn
AUTHOR
STATUS
approved