A084433 Numbers all 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

Offset

1,1

Comments

Following are members of this sequence: (1) Numbers made up of even digits (GCD >= 2). (2) Numbers with sum of digits a multiple of 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).

Links

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

Example

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.

Crossrefs

Sequence in context: A256476 A154771 A071249 * A084434 A034709 A178158

Adjacent sequences: A084430 A084431 A084432 * A084434 A084435 A084436

Keyword

base,nonn

Author

Amarnath Murthy, Jun 02 2003

Extensions

Corrected and extended by David Wasserman, Dec 28 2004

Status

approved