Numbers and me

Oct 08, 2022 01:01

When I was a kid I had a thing about numbers. Not only did I have a fair aptitude at math, but I was fascinated by the patterns I could see in numbers. And fascinated to consider, if we had 6 digits on each hand, we'd have a Base 12 number system, and all the patterns would express themselves differently. But, we have a Base 10 system and it occurs to the nerd in me that I've never written any of these observations down.

First, a note about breaking down numbers to see patterns. A number like 927 breaks down to nine, thus: 9+2+7=18, 1+8=9. Sixty-five breaks down to two, thus:6+5=11, 1+1=2.

So, here goes, starting with multiples.
The most obvious place to start is with multiples of 3. The numeral will add up to 3, 6, or 9, in that succession, ad infinitum.
3, 6, 9, 12 (3),15 (6), 18 (9), 21 (3), 24 (6), 27 (9), etc. If the numerals of any number can be added to 3, 6, or 9, it will be divisible by 3 eg: 4,710,345 is 4+7+1+0+3+4+5=24, 2+4=6. so, it should be divisible by 3.
test it: 4,710,345/3=1,570,115

Multiples of 4 start getting fun to see the pattern. First it starts with numbers adding to even, then odd, but watch the pattern (4, 8, 3, 7, 2, 6, 1, 5, 9 - starting over and continuing on)
4, 8, 12 (3), 16 (7), 20 (2), 24 (6), 28 (1), 32 (5), 36 (9), then
40, 44, 48 (3), 52 (7), 56 (2), 60 (6), 64 (1), 68 (5), 72 (9)
76, 80, 84 (3), 88 (7), 92 (2), 96 (6) 100 (1) 104 (5) 108 (9), and so on.

Next along is multiples of 5, which are boring cos they always end in 5 or zero.

Multiples of 6, the pattern goes something like this:
6, 3, 9, 6, 3, 9, all the way down the line:
6, 12, 18, 24, 30, 36, etc forever. test it: 6x17=102, 1+0+2=3, so 6x18 should add up to 9 - 6x18=108, 1+0+8=9.

Multiples of 7 give some fun patterns.
7, 5, 3, 1, then backwards through the evens 8, 6, 4, 2, before starting back to the top of the odds with 9 and continuing backwards forever:
. 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, and so on
. 7, 14, 21, 28, 35, 42, 49, 56, 63,
70, 77, 84, 91, 98 etc

multiples of 8, pretty basic:
. 8, 7, 6, 5, 4, 3, 2, 1, and so on:
. 8, 16, 24, 32, 40, 48, 56, 64, etc, next one (72) would add to 9, and then down one number at a time, in succession, over and over, forever.

everybody knows multiples of nine always add to 9, right?
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, etc.
AND the last number of the digit will successively go down one, all the way to zero, and start over.

didn't mention the 2's at the top, cos its easier to start with 3s to get the idea. Multiples of 2 alternate in sets of ten, adding to even, then odd intervals.
Attend:
. 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, and so on
. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, etc.

Then there's the thing about odd numbered intervals between Squares.
1x1=1 (the next odd number is 3)
2x2=4 1+3=4 (plus the next odd number, 5)
3x3=9 4+5=9 (plus 7)
4x4=16 9+7=16 (plus 9)
5x5=25 16+9
so if I add the previous square, 25, to the next odd number, 11, I get
6x6=36, plus the next odd number 13, and I get
7x7=49, plus the next odd number, 15, and I get
8x8=64, plus the next odd number, 17, and I get
9x9=81, plus the next odd number, 19, and I get
10x10=100, plus the next odd number, 21, and I get
11x11=121, on and on and on.

There are other patterns I've noticed, but that's enough for now.
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