A288669 -id:A288669 - cp's OEIS frontend

A288626 Numbers n such that n * (x-1)/x produces a rotation of the digits in n for some value of x.

54, 216, 324, 432, 540, 648, 756, 864, 918, 972, 2232, 4464, 4554, 5049, 5454, 5544, 6696, 7776, 8928, 9108, 11070, 19188, 21951, 22140, 22221, 29268, 33210, 38376, 43443, 43902, 44280, 44442, 55350, 56565, 57564, 58536, 65853, 66420, 66663, 73170, 76752, 77490, 77787, 80487, 81180, 86886, 87804

Offset: 1

Doug Bell, Jun 11 2017

Numbers n where n * (x-1)/x produces a rotation that would have a first digit of zero are omitted.
Where n * (x-1)/x produces a rotation, x is a factor of n.
The first term where more than one value of x produces a rotation for a(n) * (x-1)/x is a(47) = 87804: 87804 * 8/9 = 78048 and 87804 * 11/12 = 80487. The first term where more than two values of x produce a rotation is a(186) = 857142: 857142 * 1/2 = 428571, 857142 * 2/3 = 571428, and 857142 * 5/6 = 714285.
The first term where a(n) * (x-1)/x produces a rotation that itself appears in this sequence is a(4) = 432: 432 * 3/4 = 324 = a(3).
If all of the digits in a(n) <= 4, then a(n)*2 also appears; if all of the digits in a(n) <= 3, then a(n)*3 also appears; if all of the digits in a(n) <= 2, then a(n)*4 also appears. Similarly, if each of the digits in a(n) are a multiple of some number k, then a(n)/k also appears.
Where ABC represents the digits in a(n), then ABCABC, ABCABCABC, ... also appear in the sequence with the same value(s) of x.

			a(1) = 54, 54 * 5/6 = 45;
a(9) = 918, 918 * 33/34 = 891.

Doug Bell and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Doug Bell)
Doug Bell, Table of n, a(n), x/(x+1), a(n)*x/(x+1) for n = 1..1000

Cf. A034089, A288669, A285936.

ok[n_] := Block[{d = IntegerDigits[n], m, trg, t}, m = Length[d]; trg = FromDigits /@ Select[ RotateLeft[d, #] & /@ Range[m-1], First[#] > 0 &]; {} != Select[ trg, (t = n/#; Numerator[t]== 1 + Denominator[t]) &]]; Select[ Range[10^5], ok] (* Giovanni Resta, Jun 14 2017 *)

cp's OEIS Frontend

A288626 Numbers n such that n * (x-1)/x produces a rotation of the digits in n for some value of x.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica