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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) 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.)