Belgian Words
Belgian Words are words
which follow, in a certain way, the rule of the Belgian
Numbers (formerly Eric
Numbers).
What is a “Belgian
Number”? [reminder]
176 is a “Belgian number” because, starting from 0, one
can build a sequence containing 176 in this way:
0 1 8 14 15 22 28 29 36 42 43 50 ... 155 162 168 169 176. (building sequence)
1 7 6 1
7 6 1 7 6
1 7 ...
7 6 1
7 (first differences repeated pattern)
The “first differences” building rule is easy to
understand. The above example shows that you don’t have to add the full
digit-pattern [1+7+6] to produce the according Belgian number: 176
appears when 7 is added to the previous integer – not 6.
Here are the first Belgian numbers:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 17 18 20 21 22 24 26
27 30 31 33 35 36 39 40 42 44 45 48 50 53 54 55 60 62 63 66 70 71 72 77 80 81
84 88 90 93 99 100 101 102 106 108 110 111 112 114 117 120 ...
Now, let us transform
a word into a number by substituting each letter with it’s rank in the
alphabet; the word ERIC, for instance, becomes 51893:
E=5, R=18, I=9, C=3 --> ERIC = 51893
ERIC will be an Belgian
Word if and only if the number 51893 is part of the sequence which starts
with 0 and builds up step by step with the pattern E+R+I+C (5+18+9+3) been
added:
0 5 23 32 35 40 58 67
70 75 93 102... (building sequence)
E R
I C E
R I C
E R I... (first differences repeated pattern)
In the end we have:
... 51858 51867 51870
51875 51893 <--
hit! ERIC is a Belgian Word.
... I
C E R
__________
What about Self-Belgian
Word Numbers (SBWN)? Self-Belgian
Word Numbers would be Belgian Words which describe their own seed...
CINQ (five) is
such a word in French (we
have not yet searched for English ones):
First, we transform
it into a number:
C=3, I=9, N=14, Q=17 --> CINQ = 39147
Then we start the building
sequence with the according “seed” 5:
5 8 17 31
48 51 60 74 91 94 103 ... (building
sequence)
C I
N Q C
I N Q
C I ... (first differences repeated pattern)
In the end we have:
...39118 39135 39138 39147 <-- hit! CINQ is
a French SBWN.
Q
C I
VINGT (twenty,
in French) fits also:
V=22, I=9, N=14, G=7, T=20 --> VINGT = 22914720
Building sequence with seed
20 starts like this:
20 42 51 65
72 92 114 123 137 144 164 186 195 ...
V
I N G
T V I
N G T
V I ...
And in the end we
have:
...22914648 22914668
22914690 22914699 22914713 22914720
<- hit!
...
T V I
N G
TRENTE (30) is
ok, and TRENTE-QUATRE (34) too...
So 5, 20, 30, 34, ...
start a sequence of French Self-Belgian Word Numbers. How would
look the English Self-Belgian Word Numbers sequence?
(Jens Voss found the first integers under 100: 24, 28, 43, 45, 54, 70)
___________
[copyleft: E. Angelini, Brussels, Belgium –
june 15th, 2005.]
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