A084433 Numbers whose cyclic permutations have GCD > 1.

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 36, 39, 40, 42, 44, 45, 46, 48, 50, 51, 54, 55, 57, 60, 62, 63, 64, 66, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 148, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 185, 186, 189, 192, 195, 198, 200, 201, 202, 204, 206, 207, 208, 210, 213, 216

Offset: 1

Author

Amarnath Murthy, Jun 02 2003

Keywords

• base
• nonn
• changed

Comments

Following are members of this sequence: (1) Numbers made up of even digits (GCD >= 2). (2) Numbers divisible by 3 (GCD >= 3). (3) Multiples of 11 containing an even number of nonzero digits (GCD >= 11); (i) with highest common factor 11 e.g. 1243; (ii) with highest common factor > 11 e.g. 142857. (4) Numbers made up of identical digits >1 (GCD = the number itself).

Examples

			1243 and its cyclic permutations 1243, 2431, 4312, 3124 are members as all are divisible by 11.
148, 481 and 814 are members because their GCD is 37.
		

Links

• Jonathan Frech, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A287513, A387356 (complement).

Programs

Mathematica

A084433Q[k_] := GCD @@ Map[FromDigits, NestList[RotateLeft, #, Length[#] - 1] & [IntegerDigits[k]]] > 1;
Select[Range[200], A084433Q] (* Paolo Xausa, Aug 27 2025 *)

Extensions

Corrected and extended by David Wasserman, Dec 28 2004