Sum Period

M2007U-E2016-A2017-S2017-M2021_20170605x01

Definition:

We start from a natural number "n",

we sum all the digits it has and get a sum "x。", by adding n and x。 we have a result n₁

we sum all the digits of n₁, the sum is x₁, n₁ + x₁ = n₂

we sum all the digits of n₂, the sum is x₂, n₂ + x₂ = n₃ and so on...

here, I will define that: n₁ = n↓(1)

n。 + x。 = n1

n₁ + x₁ = n₂...

n↓(a) + x↓(a) = n↓(a+1)

you will find that x has a period or a pattern

Example

let's say we start with the number 128, then

128 + 11 = 139 191 + 11 = 202 236 + 11 = 247 317 + 11 = 328 398 + 20 = 418

139 + 13 =152 202 + 4 = 206 247 + 13 = 260 328 + 13 = 341 418 + 13 = 431

152 + 8 = 160 206 + 8 = 214 260 + 8 = 268 341 + 8 = 349 431 + 8 = 439

160 + 7 = 167 214 + 7 = 221 268 + 16 = 284 349 + 16 = 365 439 + 16 = 455

167 + 14 = 181 221 + 5 = 226 284 + 14 = 298 365 + 14 = 379 455 + 14 = 469

181 + 10 = 191 226 + 10 = 236 298 + 19 = 317 379 + 19 = 398 469 + 19 = 488

and so on

the numbers (represented as "n" during defining) which are the first number in their own equation

the numbers (represented as "x" during defining) which are the second number in their own equation

let's say n↓(a) = 128 , x↓(a) = 1+2+8 = 11, so n↓(a+1) = n↓(a) + x↓(a) = 128 + 11 = 139;

let's say n↓(b) = 226 , x↓(b) = 2+2+6 = 10, so n↓(b+1) = n↓(b) + x↓(b) = 226 + 10 = 236

from the 30 equations above, we know that:

x at the 1st row is likely to be 11 or 20

x at the 2nd row is likely to be 13 or 4

x at the 3rd row is likely to be 8 or other numbers

x at the 4th row is likely to be 7 or 16

x at the 5th row is likely to be 10 or 19

there is a pattern, each column is made according to a certain period or a repeating pattern.