A329135 Numbers whose differences of prime indices are an aperiodic word.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73

Offset

1,2

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 aperiodic if its cyclic rotations are all different.

Links

Table of n, a(n) for n=1..67.

Example

The sequence of terms together with their differences of prime indices begins:
    1: ()
    2: ()
    3: ()
    4: (0)
    5: ()
    6: (1)
    7: ()
    9: (0)
   10: (2)
   11: ()
   12: (0,1)
   13: ()
   14: (3)
   15: (1)
   17: ()
   18: (1,0)
   19: ()
   20: (0,2)
   21: (2)
   22: (4)

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[100], aperQ[Differences[primeMS[#]]]&]

Crossrefs

Complement of A329134.

These are the Heinz numbers of the partitions counted by A329137.

Aperiodic compositions are A000740.

Aperiodic binary words are A027375.

Numbers whose binary expansion is aperiodic are A328594.

Numbers whose prime signature is aperiodic are A329139.

Cf. A056239, A112798, A124010, A152061, A329133, A329136, A329140.

Sequence in context: A285316 A362147 A361395 * A182768 A368917 A207481

Adjacent sequences: A329132 A329133 A329134 * A329136 A329137 A329138

Keyword

nonn

Author

Gus Wiseman, Nov 09 2019

Status

approved