A375738 - OEIS

%I #5 Sep 11 2024 10:07:12

%S 2,3,6,7,11,12,13,14,15,18,19,20,21,22,23,24,29,30,31,34,35,38,39,40,

%T 41,42,43,44,45,46,47,48,51,52,53,54,55,56,57,58,59,60,61,62,63,66,67,

%U 68,69,70,71,72,73,74,75,76,77,78,79,80,83,84,85,86,87,88

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

%C Non-perfect-powers (A007916) are numbers with no proper integer roots.

%C An anti-run of a sequence is an interval of positions at which consecutive terms differ by more than one.

%e The initial anti-runs are the following, whose minima are a(n):

%e   (2)

%e   (3,5)

%e   (6)

%e   (7,10)

%e   (11)

%e   (12)

%e   (13)

%e   (14)

%e   (15,17)

%e   (18)

%e   (19)

%e   (20)

%e   (21)

%e   (22)

%e   (23)

%e   (24,26,28)

%t radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;

%t Min/@Split[Select[Range[100],radQ],#1+1!=#2&]//Most

%Y For composite numbers we have A005381, runs A008864 (except first term).

%Y For prime-powers we have A120430, runs A373673 (except first term).

%Y For squarefree numbers we have A373408, runs A072284.

%Y For nonsquarefree numbers we have A373410, runs A053806.

%Y For non-prime-powers we have A373575, runs A373676.

%Y For anti-runs of non-perfect-powers:

%Y - length: A375736

%Y - first: A375738 (this)

%Y - last: A375739

%Y - sum: A375737

%Y For runs of non-perfect-powers:

%Y - length: A375702

%Y - first: A375703

%Y - last: A375704

%Y - sum: A375705

%Y A001597 lists perfect-powers, differences A053289.

%Y A007916 lists non-perfect-powers, differences A375706.

%Y Cf. A007674, A045542, A046933, A061399, A216765, A251092, A373403, A373679, A375708, A375714.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 10 2024