A353023 Positive integers k with the property that they cannot be converted to a multiple of 11 by changing at most a single decimal digit.

545, 27272, 1818181, 636363636, 90909090909, 181818181818, 272727272727, 363636363636, 454545454545, 545454545454, 636363636363, 727272727272, 818181818181, 909090909090, 363636363636363, 81818181818181818, 7272727272727272727, 454545454545454545454

Offset

1,1

Comments

This sequence was inspired by a puzzle from David K. Butler.

Links

Table of n, a(n) for n=1..18.

Ben Weiss, Multiples of 11

Formula

a(n) = a(n - 18) * 10^22 + (a(n - 18) mod 100) * 101010101010101010101.

Prog

(OBJC)
int main(int argc, const char * argv[]) {
  // Search positive integers for solutions, up to 10^20.
  for (int length = 1; length < 20; ++length) {
    for (int a = 0; a <= 9; ++a) {
      int b = 9 - a;
      // Test number abababab... with length 'length'
      int a_mod_11 = (a * ((length + 1) / 2)) % 11;
      int b_mod_11 = (b * ((length    ) / 2)) % 11;
      int a_add = (b_mod_11 - a_mod_11 + 11) % 11;
      if (a + a_add == 10) {
        uint64_t num = 0;
        uint64_t dec = 1;
        for (int d = 0; d < length; ++d) {
          num += ((d & 1) ? b : a) * dec;
          dec *= 10;
        }
        NSLog(@"Found solution: %llu", num);
      }
    }
  }
  return 0;
}

Crossrefs

Cf. A008593 (multiples of 11).

Sequence in context: A159626 A020259 A184379 * A053327 A252537 A099008

Adjacent sequences: A353020 A353021 A353022 * A353024 A353025 A353026

Keyword

base,nonn

Author

Ben Weiss, May 15 2022

Status

approved