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A355523
Number of distinct differences between adjacent prime indices of n.
4
0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 2, 0, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 2, 1, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1
OFFSET
1,12
COMMENTS
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.
EXAMPLE
For example, the prime indices of 22770 are {1,2,2,3,5,9}, with differences (1,0,1,2,4), so a(22770) = 4.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Union[Differences[primeMS[n]]]], {n, 1000}]
CROSSREFS
Crossrefs found in the link are not repeated here.
Counting m such that A056239(m) = n and a(m) = k gives A279945.
With multiplicity we have A252736(n) = A001222(n) - 1.
The maximal difference is A286470, minimal A355524.
A287352 lists differences between 0-prepended prime indices.
A355534 lists augmented differences between prime indices.
A355536 lists differences between prime indices.
Sequence in context: A063962 A084114 A294881 * A110475 A366739 A086971
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 10 2022
STATUS
approved