A110304 Least alternating multiple of alternators.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 121, 12, 52, 14, 30, 16, 34, 18, 38, 0, 21, 418, 23, 72, 25, 52, 27, 56, 29, 30, 341, 32, 165, 34, 70, 36, 74, 38, 78, 0, 41, 210, 43, 616, 45, 92, 47, 96, 49, 50, 561, 52, 212, 54, 165, 56, 456, 58, 236, 0, 61, 434, 63, 256, 65, 858, 67, 272, 69

Offset

1,2

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..69.

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

Example

a(11) = 121 because 121 is the least multiple of 11 which is alternating.

Crossrefs

Cf. A030141, A110303, A110305.

Sequence in context: A250266 A357936 A085908 * A043315 A044912 A061378

Adjacent sequences: A110301 A110302 A110303 * A110305 A110306 A110307

Keyword

base,easy,nonn

Author

Walter Nissen, Jul 18 2005

Status

approved