cp's OEIS Frontend

A375736 Length of the n-th maximal anti-run of adjacent (increasing by more than one at a time) non-perfect-powers.

%I A375736 #7 Sep 11 2024 10:07:16
%S A375736 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,
%T A375736 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,
%U A375736 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1
%N A375736 Length of the n-th maximal anti-run of adjacent (increasing by more than one at a time) non-perfect-powers.
%C A375736 Non-perfect-powers (A007916) are numbers with no proper integer roots.
%C A375736 An anti-run of a sequence is an interval of positions at which consecutive terms differ by more than one.
%e A375736 The initial anti-runs are the following, whose lengths are a(n):
%e A375736   (2)
%e A375736   (3,5)
%e A375736   (6)
%e A375736   (7,10)
%e A375736   (11)
%e A375736   (12)
%e A375736   (13)
%e A375736   (14)
%e A375736   (15,17)
%e A375736   (18)
%e A375736   (19)
%e A375736   (20)
%e A375736   (21)
%e A375736   (22)
%e A375736   (23)
%e A375736   (24,26,28)
%t A375736 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A375736 Length/@Split[Select[Range[100],radQ],#1+1!=#2&]//Most
%Y A375736 For squarefree numbers we have A373127, runs A120992.
%Y A375736 For nonprime numbers we have A373403, runs A176246.
%Y A375736 For nonsquarefree numbers we have A373409, runs A053797.
%Y A375736 For prime-powers we have A373576, runs A373675.
%Y A375736 For non-prime-powers (exclusive) we have A373672, runs A110969.
%Y A375736 For runs instead of anti-runs we have A375702.
%Y A375736 For anti-runs of non-perfect-powers:
%Y A375736 - length: A375736 (this)
%Y A375736 - first: A375738
%Y A375736 - last: A375739
%Y A375736 - sum: A375737
%Y A375736 For runs of non-perfect-powers:
%Y A375736 - length: A375702
%Y A375736 - first: A375703
%Y A375736 - last: A375704
%Y A375736 - sum: A375705
%Y A375736 A001597 lists perfect-powers, differences A053289.
%Y A375736 A007916 lists non-perfect-powers, differences A375706.
%Y A375736 Cf. A007674, A045542, A046933, A216765, A251092, A373679, A375714.
%K A375736 nonn
%O A375736 1,2
%A A375736 _Gus Wiseman_, Sep 10 2024