A144504 3-transposable numbers.

142857, 285714, 142857142857, 285714285714, 142857142857142857, 285714285714285714, 142857142857142857142857, 285714285714285714285714, 142857142857142857142857142857, 285714285714285714285714285714, 142857142857142857142857142857142857

Offset

1,1

Comments

A positive integer x is called k-transposable if when the leftmost digit is moved into the units place, the result is equal to kx.

A number is 1-transposable iff its digits are all the same.

Kahan shows that if k>1 then k must be 3 and the only solutions are concatenations of copies of either 142857 or 285714, as given in this sequence, which therefore lists all k-transposable numbers with k>1.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20

S. Kahan, k-transposable integers, Math. Mag., 49 (1976), 27-28.

Crossrefs

Sequence in context: A101202 A323711 A306265 * A344436 A146754 A180340

Adjacent sequences: A144501 A144502 A144503 * A144505 A144506 A144507

Keyword

nonn,base

Author

N. J. A. Sloane, Dec 14 2008

Status

approved