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A375736
Length of the n-th maximal anti-run of adjacent (increasing by more than one at a time) non-perfect-powers.
14
1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
Non-perfect-powers (A007916) are numbers with no proper integer roots.
An anti-run of a sequence is an interval of positions at which consecutive terms differ by more than one.
EXAMPLE
The initial anti-runs are the following, whose lengths are a(n):
(2)
(3,5)
(6)
(7,10)
(11)
(12)
(13)
(14)
(15,17)
(18)
(19)
(20)
(21)
(22)
(23)
(24,26,28)
MATHEMATICA
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Length/@Split[Select[Range[100], radQ], #1+1!=#2&]//Most
CROSSREFS
For squarefree numbers we have A373127, runs A120992.
For nonprime numbers we have A373403, runs A176246.
For nonsquarefree numbers we have A373409, runs A053797.
For prime-powers we have A373576, runs A373675.
For non-prime-powers (exclusive) we have A373672, runs A110969.
For runs instead of anti-runs we have A375702.
For anti-runs of non-perfect-powers:
- length: A375736 (this)
- first: A375738
- last: A375739
- sum: A375737
For runs of non-perfect-powers:
- length: A375702
- first: A375703
- last: A375704
- sum: A375705
A001597 lists perfect-powers, differences A053289.
A007916 lists non-perfect-powers, differences A375706.
Sequence in context: A156144 A358235 A136044 * A184240 A244840 A103414
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 10 2024
STATUS
approved