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 A329132 Numbers whose augmented differences of prime indices are a periodic sequence. 7
 4, 8, 15, 16, 32, 55, 64, 90, 105, 119, 128, 225, 253, 256, 403, 512, 540, 550, 697, 893, 935, 1024, 1155, 1350, 1357, 1666, 1943, 2048, 2263, 3025, 3071, 3150, 3240, 3375, 3451, 3927, 3977, 4096, 4429, 5123, 5500, 5566, 6731, 7735, 8083, 8100, 8192, 9089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 sequence is periodic if its cyclic rotations are not all different. LINKS Table of n, a(n) for n=1..48. EXAMPLE The sequence of terms together with their augmented differences of prime indices begins: 4: (1,1) 8: (1,1,1) 15: (2,2) 16: (1,1,1,1) 32: (1,1,1,1,1) 55: (3,3) 64: (1,1,1,1,1,1) 90: (2,1,2,1) 105: (2,2,2) 119: (4,4) 128: (1,1,1,1,1,1,1) 225: (1,2,1,2) 253: (5,5) 256: (1,1,1,1,1,1,1,1) 403: (6,6) 512: (1,1,1,1,1,1,1,1,1) 540: (2,1,1,2,1,1) 550: (3,1,3,1) 697: (7,7) 893: (8,8) 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 May 18 15:24 EDT 2024. Contains 372664 sequences. (Running on oeis4.)