A329134 Numbers whose differences of prime indices are a periodic word.

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.

Links

Table of n, a(n) for n=1..49.

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.

Cf. A000740, A027375, A056239, A112798, A124010, A328594, A329132, A329139.

Sequence in context: A190519 A341611 A083419 * A090081 A059172 A360558

Adjacent sequences: A329131 A329132 A329133 * A329135 A329136 A329137

Keyword

nonn

Author

Gus Wiseman, Nov 09 2019

Status

approved