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

Author

Walter Nissen, Jul 18 2005

Keywords

• base
• easy
• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A030141, A110303, A110305.