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 A329133 Numbers whose augmented differences of prime indices are an aperiodic sequence. 6
 1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The augmented differences aug(y) of an integer partition y of length k are given by aug(y)_i = y_i - y_{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3). 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 finite sequence is aperiodic if its cyclic rotations are all different. LINKS EXAMPLE The sequence of terms together with their augmented differences of prime indices begins: 1: () 2: (1) 3: (2) 5: (3) 6: (2,1) 7: (4) 9: (1,2) 10: (3,1) 11: (5) 12: (2,1,1) 13: (6) 14: (4,1) 17: (7) 18: (1,2,1) 19: (8) 20: (3,1,1) 21: (3,2) 22: (5,1) 23: (9) 24: (2,1,1,1) 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]; aug[y_]:=Table[If[i

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Last modified March 31 18:05 EDT 2023. Contains 361672 sequences. (Running on oeis4.)