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A373403 Length of the n-th maximal antirun of composite numbers differing by more than one.

%I A373403 #17 Jun 12 2024 16:17:08
%S A373403 3,1,3,1,3,1,2,1,1,1,3,1,1,1,2,1,3,1,2,1,1,1,2,1,1,1,3,1,1,1,2,1,3,1,
%T A373403 1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,3,1,3,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,
%U A373403 2,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,2,1,1
%N A373403 Length of the n-th maximal antirun of composite numbers differing by more than one.
%C A373403 This antirun ranges from A005381 (with 4 prepended) to A068780, with sum A373404.
%C A373403 An antirun of a sequence (in this case A002808) is an interval of positions such that consecutive terms differ by more than one.
%H A373403 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%F A373403 a(2n) = 1.
%F A373403 a(2n - 1) = A196274(n) for n > 1.
%e A373403 Row-lengths of:
%e A373403    4   6   8
%e A373403    9
%e A373403   10  12  14
%e A373403   15
%e A373403   16  18  20
%e A373403   21
%e A373403   22  24
%e A373403   25
%e A373403   26
%e A373403   27
%e A373403   28  30  32
%e A373403   33
%e A373403   34
%e A373403   35
%e A373403   36  38
%e A373403   39
%e A373403   40  42  44
%t A373403 Length/@Split[Select[Range[100],CompositeQ],#1+1!=#2&]//Most
%Y A373403 Functional neighbors: A005381, A027833 (partial sums A029707), A068780, A176246 (rest of A046933, firsts A073051), A373127, A373404, A373409.
%Y A373403 A000040 lists the primes, differences A001223.
%Y A373403 A046933 counts composite numbers between primes.
%Y A373403 A065855 counts composite numbers up to n.
%Y A373403 Cf. A005117, A038664, A053767, A067970, A174965, A196274, A373400, A373573.
%K A373403 nonn
%O A373403 1,1
%A A373403 _Gus Wiseman_, Jun 05 2024