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A329134
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Numbers whose differences of prime indices are a periodic word.
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8
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8, 16, 27, 30, 32, 64, 81, 105, 110, 125, 128, 180, 210, 238, 243, 256, 273, 343, 385, 450, 506, 512, 625, 627, 729, 806, 935, 1001, 1024, 1080, 1100, 1131, 1155, 1331, 1394, 1495, 1575, 1729, 1786, 1870, 1887, 2048, 2187, 2197, 2310, 2401, 2431, 2451, 2635
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
A sequence is periodic if its cyclic rotations are not all different.
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LINKS
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EXAMPLE
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The sequence of terms together with their differences of prime indices begins:
8: (0,0)
16: (0,0,0)
27: (0,0)
30: (1,1)
32: (0,0,0,0)
64: (0,0,0,0,0)
81: (0,0,0)
105: (1,1)
110: (2,2)
125: (0,0)
128: (0,0,0,0,0,0)
180: (0,1,0,1)
210: (1,1,1)
238: (3,3)
243: (0,0,0,0)
256: (0,0,0,0,0,0,0)
273: (2,2)
343: (0,0)
385: (1,1)
450: (1,0,1,0)
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];
Select[Range[10000], !aperQ[Differences[primeMS[#]]]&]
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CROSSREFS
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These are the Heinz numbers of the partitions counted by A329144.
Numbers whose binary expansion is periodic are A121016.
Numbers whose prime signature is periodic are A329140.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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