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A288626 Numbers n such that n * (x-1)/x produces a rotation of the digits in n for some value of x. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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

EXAMPLE

a(1) = 54, 54 * 5/6 = 45;

a(9) = 918, 918 * 33/34 = 891.

MATHEMATICA

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 *)

CROSSREFS

Cf. A034089, A288669, A285936.

Sequence in context: A248598 A157428 A187299 * A124007 A221867 A248209

Adjacent sequences:  A288623 A288624 A288625 * A288627 A288628 A288629

KEYWORD

nonn,base

AUTHOR

Doug Bell, Jun 11 2017

STATUS

approved

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Last modified January 15 12:14 EST 2021. Contains 340187 sequences. (Running on oeis4.)