# Kekule number

A pedigree in Michael von Aitzing's work Thesaurus principum hac aetate in Europa viventium , Cologne 1590, p. 146f., Shows King Heinrich III. of France as n ° 1 with its ancestors n ° 2 to n ° 31

The Kekule number , also called numbering according to the Sosa-Stradonitz system or Sosa number for short , denotes the number of a person in an ancestral list or pedigree according to Stephan Kekule von Stradonitz . This numbering, which has established itself internationally, was used as early as 1590 by Michael von Aitzing , then in 1676 by Hieronymus de Sosa and in 1883 by Francis Galton .

The Family will receive regardless of gender, the number 1, his father the number 2, the mother the number 3. If a person has the number n (z. B. 2 for the father), then whose father is assigned the number 2 · n (ie Doubling and thus the number 4 for the paternal grandfather of the test person), the mother 2 · n + 1 (here the 5). The father of 10 gets the number 20, the mother gets the number 21.

All male ancestors have even numbers, all female ancestors have odd numbers.

The following numbers are assigned to the test person and the ancestor generations I to IV:

Generation 0                                   1
(Proband)                        ______________|________________
|                               |
Generation I                    2                               3
(Eltern)                 _______|_______                 _______|_______
|               |               |               |
Generation II           4               5               6               7
(Großeltern)         ___|___         ___|___         ___|___         ___|___
|       |       |       |       |       |       |       |
Generation III      8       9      10      11      12      13      14      15
(Urgroßeltern)     _|_     _|_     _|_     _|_     _|_     _|_     _|_     _|_
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
Generation IV    16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31


Due to the loss of ancestors it is possible that some of the ancestors receive several Kekule numbers.

## properties

The generation number can be determined from each Kekule number using the logarithm to base 2: ${\ displaystyle {x}}$

${\ displaystyle {\ text {Generation}} (x) = \ lfloor \ log _ {2} x \ rfloor}$

It is assumed here that generation 0 represents the test person (Kekule No. 1).

Other relationships are:

${\ displaystyle {\ text {Kind}} (x) = \ lfloor x / 2 \ rfloor}$
${\ displaystyle {\ text {father}} (x) = 2x}$
${\ displaystyle {\ text {mother}} (x) = 2x + 1}$

Number of relatives when looking at generations: ${\ displaystyle h}$

${\ displaystyle {\ text {use}} (h) = 2 ^ {h} -1}$

## Other uses

Kekule numbering is used in computer science to efficiently address binary tree nodes in an array . This data structure is used, for example, to implement a heap , which is the basis for the heapsort sorting method . In contrast to genealogy , however, in a binary tree the parent nodes are referred to as child nodes and the child nodes as parent nodes.