A110305 Factors of alternators which produce least alternating multiples.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 4, 1, 2, 1, 2, 1, 2, 0, 1, 19, 1, 3, 1, 2, 1, 2, 1, 1, 11, 1, 5, 1, 2, 1, 2, 1, 2, 0, 1, 5, 1, 14, 1, 2, 1, 2, 1, 1, 11, 1, 4, 1, 3, 1, 8, 1, 4, 0, 1, 7, 1, 4, 1, 13, 1, 4, 1, 1, 11, 1, 4, 1, 6, 1, 5, 1, 6, 0, 1, 5, 1, 3, 1, 3, 1, 7, 1, 1, 12, 1, 18, 1, 23, 1, 34, 1, 111, 0

Offset

1,11

Comments

An alternating integer is a positive integer for which, in base-10, the parity of its digits alternates. E.g. 121 is alternating because its consecutive digits are odd-even-odd, 1 being odd and 2 even. Of course, 1234567890 is also alternating. An alternator is a positive integer which has a multiple which is alternating.

For n congruent to 0 mod 20, a(n) is shown as zero to indicate that n is not an alternator.

Links

Table of n, a(n) for n=1..100.

45th International Mathematical Olympiad (45th IMO), Problem #6 and Solution, Mathematics Magazine, 2005, Vol. 78, No. 3, pp. 247, 250-251.

Example

a(13) is 4 because the least multiple of 13 which is alternating is 52, which is 13 * 4. Of course 13, 26 and 39 are not alternating. 52 is alternating because 5 is odd and 2 is even.

Crossrefs

Cf. A030141, A110303, A110304.

Sequence in context: A307245 A204846 A127991 * A010199 A010200 A086320

Adjacent sequences: A110302 A110303 A110304 * A110306 A110307 A110308

Keyword

base,easy,nonn

Author

Walter Nissen, Jul 18 2005

Status

approved