A373410 - OEIS

%I #7 Jun 07 2024 08:04:51

%S 4,9,25,28,45,49,50,64,76,81,99,100,117,121,125,126,136,148,153,169,

%T 172,176,189,208,225,243,244,245,261,276,280,289,297,316,325,333,343,

%U 344,351,352,361,364,369,376,388,405,424,425,441,460,476,477,496,508,513

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

%C The maximum is given by A068781.

%C An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.

%C Consists of 4 and all nonsquarefree numbers n such that n - 1 is also nonsquarefree.

%H Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>

%F a(1) = 4; a(n>1) = A068781(n-1) + 1.

%e Row-minima of:

%e    4   8

%e    9  12  16  18  20  24

%e   25  27

%e   28  32  36  40  44

%e   45  48

%e   49

%e   50  52  54  56  60  63

%e   64  68  72  75

%e   76  80

%e   81  84  88  90  92  96  98

%e   99

%t First/@Split[Select[Range[100],!SquareFreeQ[#]&],#1+1!=#2&]

%Y Functional neighbors: A005381, A006512, A053806, A068781, A373408, A373409, A373412.

%Y A005117 lists the squarefree numbers, first differences A076259.

%Y A013929 lists the nonsquarefree numbers, first differences A078147.

%Y Cf. A049094, A061399, A077641, A077643, A112926, A143658, A294242, A350842, A372683, A372684, A373125.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 06 2024