Tamatobe function is my function used to create a sum of numbers multiplied by 100, rounding to the nearest multiple of 125, and divide them by 125 recursively. The function symbol is denoted with the letter ₸ (Kazakhstani tenge symbol, U+20B8).
Tamatobe function is defined as:
₸(n) = ₸(|n|) where |n| denotes the absolute value.
Multiply the original number by 100.
If the original number multiplied by 100 is not divisible by 100, find the nearest multiple of 125, and calculate the difference in terms of absolute value divided by 25. Take the difference into the summation field.
Divide the number by 125, resulting number after dividing by 125 and add into the summation field, and repeat the process until the number is reduced to integers from -2 to 2. If the original number multiplied by 100 is already divisible by 100, multiply the number added into the summation field in this rule by 2.
Once the number is reduced to integers from -2 to 2, end the recursion process. Take the square of the final result in the summation field.
There are special definitions: for ₸(n) for n = -2, -1, 0, 1, 2
₸(0) = 0
₸(1) = 2^2 = 4
₸(2) = 4^2 = 16
₸(5)
⇒ Step 1.1: n = 500, k = 0
⇒ Step 1.2: n = 4, k = 4 × 2 = 8
⇒ Step 2.1: n = 400, k = 8
⇒ Step 2.2: n = 375, Δ = 25, k = 8 + 1 = 9
⇒ Step 2.3: n = 3, k = 9 + 3 = 12
⇒ Step 3.1: n = 300, k = 12
⇒ Step 3.2: n = 250, Δ = 50, k = 12 + 2 = 14
⇒ Step 3.3: n = 2, k = 14 + 2 = 16
⇒ Step 4: 16^2 = 256
Final result: ₸(5) = 256
₸(13)
⇒ Step 1.1: n = 1300, k = 0
⇒ Step 1.2: n = 1250, Δ = 50, k = 2
⇒ Step 1.3: n = 10, k = 2 + 10 = 12
⇒ Step 2.1: n = 1000, k = 12
⇒ Step 2.2: n = 8, k = 12 + 8 × 2 = 12 + 16 = 28
⇒ Step 3.1: n = 800, k = 28
⇒ Step 3.2: n = 750, Δ = 50, k = 28 + 2 = 30
⇒ Step 3.3: n = 6, k = 30 + 6 = 36
⇒ Step 4.1: n = 600, k = 36
⇒ Step 4.2: n = 625, Δ = 25, k = 36 + 1 = 37
⇒ Step 4.3: n = 5, k = 37 + 5 = 42
⇒ Step 5.1: n = 500, k = 42
⇒ Step 5.2: n = 4, k = 42 + 4 × 2 = 42 + 8 = 50
⇒ Step 6.1: n = 400, k = 50
⇒ Step 6.2: n = 375, Δ = 25, k = 50 + 1 = 51
⇒ Step 6.3: n = 3, k = 51 + 3 = 54
⇒ Step 7.1: n = 300, k = 54
⇒ Step 7.2: n = 250, Δ = 50, k = 54 + 2 = 56
⇒ Step 7.3: n = 2, k = 56 + 2 = 58
⇒ Step 8: 58^2 = 3,364
Final result: ₸(13) = 3,364
₸(67)
⇒ Step 1: n = 6700 ⇒ n = 6750, Δ = 50 ⇒ n = 54 ⇒ k = 56
⇒ Step 2: n = 5400 ⇒ n = 5375, Δ = 25 ⇒ n = 43 ⇒ k = 100
⇒ Step 3: n = 4300 ⇒ n = 4250, Δ = 50 ⇒ n = 34 ⇒ k = 136
⇒ Step 4: n = 3400 ⇒ n = 3375, Δ = 25 ⇒ n = 27 ⇒ k = 164
⇒ Step 5: n = 2700 ⇒ n = 2750, Δ = 50 ⇒ n = 22 ⇒ k = 188
⇒ Step 6: n = 2200 ⇒ n = 2250, Δ = 50 ⇒ n = 18 ⇒ k = 208
⇒ Step 7: n = 1800 ⇒ n = 1750, Δ = 50 ⇒ n = 14 ⇒ k = 224
⇒ Step 8: n = 1400 ⇒ n = 1375, Δ = 25 ⇒ n = 11 ⇒ k = 236
⇒ Step 9: n = 1100 ⇒ n = 1125, Δ = 25 ⇒ n = 9 ⇒ k = 246
⇒ Step 10: n = 900 ⇒ n = 875, Δ = 25 ⇒ n = 7 ⇒ k = 254
⇒ Step 11: n = 700 ⇒ n = 750, Δ = 50 ⇒ n = 6 ⇒ k = 262
⇒ Step 12: n = 600 ⇒ n = 625, Δ = 25 ⇒ n = 5 ⇒ k = 268
⇒ Step 13: n = 500 ⇒ n = 500, Δ = 0 ⇒ n = 4 [×2] ⇒ k = 276
⇒ Step 14: n = 400 ⇒ n = 375, Δ = 25 ⇒ n = 3 ⇒ k = 280
⇒ Step 15: n = 300 ⇒ n = 250, Δ = 50 ⇒ n = 2 ⇒ k = 284
⇒ Step 16: 284^2 = 80,656
Final result: ₸(67) = 80,656