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A335432
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Number of anti-run permutations of the prime indices of Mersenne numbers A000225(n) = 2^n - 1.
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4
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1, 1, 1, 2, 1, 1, 1, 6, 2, 6, 2, 36, 1, 6, 6, 24, 1, 24, 1, 240, 6, 24, 2, 1800, 6, 6, 6, 720, 6, 1800, 1, 120, 24, 6, 24, 282240, 2, 6, 24, 15120, 2, 5760, 6, 5040, 720, 24, 6, 1451520, 2, 5040, 120, 5040, 6, 1800, 720, 40320, 24, 720, 2, 1117670400, 1, 6, 1800, 5040, 6
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OFFSET
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1,4
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COMMENTS
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An anti-run is a sequence with no adjacent equal parts.
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.
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(10) = 6 permutations:
() (2) (4) (2,3) (11) (2,4,2) (31) (2,3,7) (21,4) (11,2,5)
(3,2) (2,7,3) (4,21) (11,5,2)
(3,2,7) (2,11,5)
(3,7,2) (2,5,11)
(7,2,3) (5,11,2)
(7,3,2) (5,2,11)
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Permutations[primeMS[2^n-1]], !MatchQ[#, {___, x_, x_, ___}]&]], {n, 0, 30}]
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PROG
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CROSSREFS
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The version for factorial numbers is A335407.
Permutations of prime indices are A008480.
Separable partitions are ranked by A335433.
Inseparable partitions are ranked by A335448.
Anti-run permutations of prime indices are A335452.
Strict permutations of prime indices are A335489.
Mersenne numbers: A000225, A046051, A046800, A046801, A049093, A059305, A159611, A325610, A325611, A325612, A325625.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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