digital-root.js

// https://jsfiddle.net/erkobridee/56nwr3d2/1/

/*
  references

  Digital Root | Math is Fun
  https://www.mathsisfun.com/numbers/digital-root.html
  
  Digital Root Calculator | Omni Calculator
  https://www.omnicalculator.com/math/digital-root
*/

const calcDigitRootOptimized = n => --n % 9 + 1;

const calcDigitRoot = n => {
  if(n === 10) return 1;
  if(n < 10) return n;
  return calcDigitRoot((''+n).split('').reduce((acc, d) => acc + Number(d), 0));
}

//------------------------------------------------------------------------//

// number to string
const n2s = value => ''+value;
// string to characteres (digits)  array
const s2a = value => n2s(value).split('');

const showDigitRootCalcSteps = n => {
  if(n < 10) return n2s(n);

  const steps = [];

  let result = n;
  do {
    const digitsArray = s2a(result);
    result = digitsArray.reduce((acc, digit) => acc + Number(digit), 0);
    steps.push(`( ${digitsArray.join(' + ')} ) = ${result}`)
  } while( result > 10 );
  
  return `${n} ${steps.join(' ')}`;
}

//------------------------------------------------------------------------//

const inputValue = 9999;

const results = {
  calcDigitRootOptimized: calcDigitRootOptimized(inputValue),
  calcDigitRoot: calcDigitRoot(inputValue),
  showDigitRootCalcSteps: showDigitRootCalcSteps(9999)
}

console.log(
  `digit root value of ${inputValue} = `, results
);

/*
  output:

  "digit root value of 9999 = ", {
    calcDigitRoot: 9,
    calcDigitRootOptimized: 9,
    showDigitRootCalcSteps: "9999 ( 9 + 9 + 9 + 9 ) = 36 ( 3 + 6 ) = 9"
  }

*/