A110303 Alternators.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

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.

This sequence is the answer to the 6th problem proposed the 2nd day by Iran during the 45th International Mathematical Olympiad, in Athens (Greece), 2004 (see links). - Bernard Schott, Apr 12 2021

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10001 (adapted to offset by Michel Marcus)

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

The IMO Compendium, Problem 6, 45th IMO 2004.

Index to sequences related to Olympiads.

Formula

Positive n, not congruent to 0 mod 20.

a(n + 19) = a(n) + 20. - David A. Corneth, Apr 13 2021

Example

11 is an alternator and in the sequence because it has a multiple which is alternating. The least of these multiples is 121.

Mathematica

Select[Range[75], Mod[#, 20] != 0 &] (* Michael De Vlieger, Apr 13 2021 *)

Crossrefs

Cf. A030141, A030142, A110304, A110305, A008602 (complement), A343335, A343336.

Sequence in context: A051108 A051107 A338265 * A347520 A180493 A346132

Adjacent sequences: A110300 A110301 A110302 * A110304 A110305 A110306

Keyword

base,easy,nonn

Author

Walter Nissen, Jul 18 2005

Extensions

Offset 1 from Michel Marcus, May 12 2021

Status

approved