VOOZH about

URL: https://oeis.org/A329134

⇱ A329134 - OEIS

login
A329134
Numbers whose differences of prime indices are a periodic word.
8
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
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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)
MATHEMATICA
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[#]]]&]
CROSSREFS
Complement of A329135.
These are the Heinz numbers of the partitions counted by A329144.
Periodic binary words are A152061.
Periodic compositions are A178472.
Numbers whose binary expansion is periodic are A121016.
Numbers whose prime signature is periodic are A329140.
Sequence in context: A190519 A341611 A083419 * A090081 A059172 A360558
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 09 2019
STATUS
approved