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A373410 Minimum of the n-th maximal antirun of nonsquarefree numbers differing by more than one.

%I A373410 #7 Jun 07 2024 08:04:51
%S A373410 4,9,25,28,45,49,50,64,76,81,99,100,117,121,125,126,136,148,153,169,
%T A373410 172,176,189,208,225,243,244,245,261,276,280,289,297,316,325,333,343,
%U A373410 344,351,352,361,364,369,376,388,405,424,425,441,460,476,477,496,508,513
%N A373410 Minimum of the n-th maximal antirun of nonsquarefree numbers differing by more than one.
%C A373410 The maximum is given by A068781.
%C A373410 An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.
%C A373410 Consists of 4 and all nonsquarefree numbers n such that n - 1 is also nonsquarefree.
%H A373410 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%F A373410 a(1) = 4; a(n>1) = A068781(n-1) + 1.
%e A373410 Row-minima of:
%e A373410    4   8
%e A373410    9  12  16  18  20  24
%e A373410   25  27
%e A373410   28  32  36  40  44
%e A373410   45  48
%e A373410   49
%e A373410   50  52  54  56  60  63
%e A373410   64  68  72  75
%e A373410   76  80
%e A373410   81  84  88  90  92  96  98
%e A373410   99
%t A373410 First/@Split[Select[Range[100],!SquareFreeQ[#]&],#1+1!=#2&]
%Y A373410 Functional neighbors: A005381, A006512, A053806, A068781, A373408, A373409, A373412.
%Y A373410 A005117 lists the squarefree numbers, first differences A076259.
%Y A373410 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373410 Cf. A049094, A061399, A077641, A077643, A112926, A143658, A294242, A350842, A372683, A372684, A373125.
%K A373410 nonn
%O A373410 1,1
%A A373410 _Gus Wiseman_, Jun 06 2024