OFFSET
1,1
COMMENTS
Numbers n where n * x/(x-1) produces a rotation that would have a first digit of zero are omitted.
Where n * x/(x-1) produces a rotation, (x-1) is a factor of n.
The first term where more than one value of x produces a rotation for a(n) * x/(x-1) is a(44) = 78048: 78048 * 9/8 = 87804 and 78048 * 33/32 = 80487.
The first term where a(n) * x/(x-1) produces a rotation that itself appears in this sequence is a(3) = 243: 243 * 4/3 = 324 = a(4).
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) = 45, 45 * 6/5 = 54;
a(11) = 2223, 2223 * 248/247 = 2232.
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
KEYWORD
nonn,base
AUTHOR
Doug Bell, Jun 13 2017
STATUS
approved