Minimum positive multiple in base 10 using only 0 and 1

Based on the Sage code by Eric M. Schmidt, which in turn is based on C code by Rick Heylen.

func find_B10(n, b=10) {

    return 0 if (n == 0)

    var P = n.of(-1)
    for (var m = 0; P[0] == -1; ++m) {

        for r in (0..n) {

            next if (P[r] == -1)
            next if (P[r] ==  m)

            with ((powmod(b, m, n) + r) % n) { |t|
                P[t] = m if (P[t] == -1)
            }
        }
    }

    var R = 0
    var r = 0

    do {
        R += b**P[r]
        r = (r - powmod(b, P[r], n))%n
    } while (r > 0)

    return R
}

printf("%5s: %28s  %s\n", 'Number', 'B10', 'Multiplier')

for n in (1..10, 95..105, 297, 576, 594, 891, 909, 999, 1998, 2079, 2251, 2277, 2439, 2997, 4878) {
    printf("%6d: %28s  %s\n", n, var a = find_B10(n), a/n)
}

Output:

Number:                          B10  Multiplier
     1:                            1  1
     2:                           10  5
     3:                          111  37
     4:                          100  25
     5:                           10  2
     6:                         1110  185
     7:                         1001  143
     8:                         1000  125
     9:                    111111111  12345679
    10:                           10  1
    95:                       110010  1158
    96:                     11100000  115625
    97:                     11100001  114433
    98:                     11000010  112245
    99:           111111111111111111  1122334455667789
   100:                          100  1
   101:                          101  1
   102:                      1000110  9805
   103:                     11100001  107767
   104:                      1001000  9625
   105:                       101010  962
   297:          1111011111111111111  3740778151889263
   576:              111111111000000  192901234375
   594:         11110111111111111110  18703890759446315
   891:          1111111111111111011  1247038284075321
   909:          1011111111111111111  1112333455567779
   999:  111111111111111111111111111  111222333444555666777889
  1998: 1111111111111111111111111110  556111667222778333889445
  2079:       1001101101111111111111  481530111164555609
  2251:                 101101101111  44913861
  2277:         11110111111111111011  4879275850290343
  2439:   10000101011110111101111111  4100082415379299344449
  2997: 1111110111111111111111111111  370740777814851888925963
  4878:  100001010111101111011111110  20500412076896496722245

Last updated