Saturday, November 27, 2021

Casio fx-CG50: Integer Digit Operations

Casio fx-CG50: Integer Digit Operations


Sum of the Digits and Digital Sum with Memory


The sum of the digits is pretty much a straight forward calculation, separate all the digits and add them up.  Example:


N = 18,283


Sum of the digits: S = 1 + 8 + 2 + 8 + 3 = 22


Ernesto Estrada, author of the article "Integer-Digit Functions: An Example of Math-Art Integration" (see the Source Section below), introduces the sum of the digits with memory, which is defined as:


F = N × S 


Going with our example, N = 18,283.  With S = 22,


F = 18,283 × 22 = 402,226


The program INTDGT, programmed on the Casio fx-CG50, calculates the sum of a digits of a positive integer and the digital sum of the memory.


Variables:

N = input

S = sum of the digits

F = digital sum with memory

List 1 = list where each element is a digit of N


Casio fx-CG50 Program:  INTDGT


"2021-09-21 EWS"

"N>0, INTEGER "? → N

N → A

Int log N → L

Seq(0,x,0,L,1) → List 1

For 1 → K To L+1

Int (A÷10^L) → List 1[K]

A-List 1[K]×10^L → A

L-1 → L

Next

Sum List 1→ S

S×N → F

"SUM OF DIGITS="

S ◢

"S×N="

F ◢

"DIGITS IN List 1"

List 1


Sum of Digits as Functions Applied to Each Digit


The program FNDGT calculates the sum of each digit and returns a list in a four element list:


{ Σ (n_k),  Σ (n_k)^2,  Σ sin(n_k), Σ cos(n_k) }


Radians angle mode is used.  The results are stored in List 2.


Casio fx-CG50 Program:  FNDGT


"2021-09-21 EWS"

Rad

"N>0, INTEGER"? → N

N → A

Int log N → L

{0,0,0,0} → List 2

For L → K To 0 Step -1

Int (A÷10^K) → M

List 2[1] + M → List 2[1]

List 2[2] + M^2 → List 2[2]

List 2[3] + sin M → List 2[3]

List 2[4] + cos M → List 2[4]

A - M×10^K → A

Next

"K, K^2, sin K, cos K" ◢

List 2


Example: 

N = 93,259


Results:

{ 28, 200, 0.9157301307, -2.944737671 }


Integers and Art


I encourage everyone to read the article listed in the source section below.   Ernesto Estrada demonstrates how to turn the sum of a digits and applying functions to the digits into beautiful art:   grass, fish, asteroids, butterflies, and other beautiful patterns.  If you have the chance, get this article while it is Open Access!  


Source:


Estrada, Ernesto  "Integer-Digit Functions:  An Example of Math-Art Integration"  The Authors, Volume 40, Number 1, 2018.   https://link.springer.com/article/10.1007%2Fs00283-017-9726-x

Retrieved September 15, 2021.   Open Access*


*as of 9/15/2021 


In a few days the 2021 calendar will just be one page.


Eddie


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