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A355524
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Minimal difference between adjacent prime indices of n > 1, or 0 if n is prime.
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13
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0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 5, 0, 0, 0, 1, 0, 0, 3, 6, 1, 0, 0, 7, 4, 0, 0, 1, 0, 0, 0, 8, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 6, 9, 0, 0, 0, 10, 0, 0, 3, 1, 0, 0, 7, 1, 0, 0, 0, 11, 0, 0, 1, 1, 0, 0, 0, 12, 0, 0, 4, 13, 8
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OFFSET
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2,9
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COMMENTS
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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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EXAMPLE
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The prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 3.
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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[If[PrimeQ[n], 0, Min@@Differences[primeMS[n]]], {n, 2, 100}]
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CROSSREFS
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Crossrefs found in the link are not repeated here.
Positions of first appearances are A077017 w/o the first term.
Positions of terms > 0 are A120944.
Positions of terms > 1 are A325161.
If singletons (k) have minimal difference k we get A355525.
Prepending 0 to the prime indices gives A355528.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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