A287513 -id:A287513 - cp's OEIS frontend

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

Amarnath Murthy, Jun 02 2003

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).

			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.

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

Cf. A287513, A387356 (complement).

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

Corrected and extended by David Wasserman, Dec 28 2004

cp's OEIS Frontend

A084433 Numbers whose cyclic permutations have GCD > 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions