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

%I A329134 #5 Nov 09 2019 16:26:06
%S A329134 8,16,27,30,32,64,81,105,110,125,128,180,210,238,243,256,273,343,385,
%T A329134 450,506,512,625,627,729,806,935,1001,1024,1080,1100,1131,1155,1331,
%U A329134 1394,1495,1575,1729,1786,1870,1887,2048,2187,2197,2310,2401,2431,2451,2635
%N A329134 Numbers whose differences of prime indices are a periodic word.
%C A329134 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.
%C A329134 A sequence is periodic if its cyclic rotations are not all different.
%e A329134 The sequence of terms together with their differences of prime indices begins:
%e A329134      8: (0,0)
%e A329134     16: (0,0,0)
%e A329134     27: (0,0)
%e A329134     30: (1,1)
%e A329134     32: (0,0,0,0)
%e A329134     64: (0,0,0,0,0)
%e A329134     81: (0,0,0)
%e A329134    105: (1,1)
%e A329134    110: (2,2)
%e A329134    125: (0,0)
%e A329134    128: (0,0,0,0,0,0)
%e A329134    180: (0,1,0,1)
%e A329134    210: (1,1,1)
%e A329134    238: (3,3)
%e A329134    243: (0,0,0,0)
%e A329134    256: (0,0,0,0,0,0,0)
%e A329134    273: (2,2)
%e A329134    343: (0,0)
%e A329134    385: (1,1)
%e A329134    450: (1,0,1,0)
%t A329134 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A329134 aperQ[q_]:=Array[RotateRight[q,#1]&,Length[q],1,UnsameQ];
%t A329134 Select[Range[10000],!aperQ[Differences[primeMS[#]]]&]
%Y A329134 Complement of A329135.
%Y A329134 These are the Heinz numbers of the partitions counted by A329144.
%Y A329134 Periodic binary words are A152061.
%Y A329134 Periodic compositions are A178472.
%Y A329134 Numbers whose binary expansion is periodic are A121016.
%Y A329134 Numbers whose prime signature is periodic are A329140.
%Y A329134 Cf. A000740, A027375, A056239, A112798, A124010, A328594, A329132, A329139.
%K A329134 nonn
%O A329134 1,1
%A A329134 _Gus Wiseman_, Nov 09 2019