Euler-26.js

// this problem has nothing to do with programming, instead with math
// first function calculates the cycle length, since the recurrence ALWAYS ends with 1
function cycleLength (b) {
  var a = 1
  var t = 0
  do {
    a = a * 10 % b
    t++
  } while (a !== 1)
  return t
}
// we do not need to check all numbers, since only specific primes give requrent period longer than 1, aka
// Full reptend primes (A001913 sequence)
function reciprocalCycles (n) {
  const originalPrimes = [7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
    73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157,
    163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241,
    251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347,
    349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439,
    443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
    557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643,
    647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751,
    757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859,
    863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977,
    983, 991, 997]
  var primes = originalPrimes.filter(el => el < n + 1)
  var max = 0
  var maxPeriod = 0
  for (var i = 0; i < primes.length; i++) {
    var tmp = cycleLength(primes[i])
    if (max < tmp) {
      maxPeriod = primes[i]
      max = tmp
    }
  }
  return maxPeriod
}
reciprocalCycles(1000)