nth in joined Demlo Number String

findNthInJoinedDemloNumber.js

// What's the 2000th digit in
// 1121123211234321123454321...?

// Assumption:
// Assume it's a number of joined demlo number, https://mathworld.wolfram.com/DemloNumber.html
// find the nth digit in the number.

function findNthDigitInJoinedDemloNumber(n) {
  // find the rowIndex of demlo number and the charAtIndex of that number
  const rowIndex = Math.ceil(Math.sqrt(n));
  const lengthOfDemloNumber = rowIndex * 2 - 1;
  const charAtIndex = lengthOfDemloNumber - (Math.pow(rowIndex, 2) - n);
  
  // get the demlo number
  const demloNumber = getDemloNumberbyIndex(rowIndex);
  const stringDemloNumber = String(demloNumber).endsWith('n') // bigint
    ? String(demloNumber).slice(0, -1)
    : String(demloNumber);
  const digit = stringDemloNumber.charAt(charAtIndex - 1);
  // console.log(rowIndex, charAtIndex, demloNumber, digit);
  console.log(`the ${n}th digit is ${digit}`);
  return digit;
}

function getDemloNumberbyIndex(rowIndex) {
  const repunit = (10n ** BigInt(rowIndex) - 1n) / 9n; // https://mathworld.wolfram.com/Repunit.html
  // console.log(repunit)
  return repunit * repunit;
}

findNthDigitInJoinedDemloNumber(2000); //8