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Unhappy Numbers Dice 3d printed

DIGITAL PREVIEW
Not a Photo

White Strong & Flexible Polished
Unhappy Numbers Dice 3d printed
Unhappy Numbers Dice 3d printed

DIGITAL PREVIEW
Not a Photo

Unhappy Numbers Dice

OVERVIEW
  • 3D printed in White Strong & Flexible Polished: White nylon plastic polished to reveal a smooth matte finish.
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  • This product is intended for mature audiences.
$4.75
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Product Description

Happy numbers are integers that reach a steady state value of 1 under the repeated procedure of squaring and adding the digits.  For example, 1366 is a happy number because 1^2 + 3^2 + 6^2 + 6^2 = 82, which leads to 8^2 + 2^2 = 68, which leads to 6^2 + 8^2 = 100, which finally leads to 1^2 + 0^2 + 0^2 = 1.

If a number doesn't reach 1 under this algorithm, it is called an unhappy number.  Unhappy numbers instead converge to a cycle of length 8.  This cycle is 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 ... For example, 1367 is an unhappy number because 1^2 + 3^2 + 6^2 + 7^2 = 95, which leads to 9^2 + 5^2 = 106, which leads to 1^2 + 0^2 + 6^2 = 37, and 37 is an element of the unhappy number cycle.

This is an 8-sided octahedral die labeled with the unhappy number cycle. It does not any obvious practical use as a die for games. If you take the modulo 8 values of the numbers you get {4, 0, 5, 2, 1, 1, 2, 4}.

 

(For more info see also this more detailed explanation of happy numbers, the happy number sequence in the OEIS, this happy number calculator, and this paper on the density of happy numbers.)

What's in the Box
INCM
Unhappy Numbers Dice
White Strong & Flexible Polished
Width
2.0 cm
Height
2.0 cm
Depth
2.0 cm
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