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A373404 Sum of the n-th maximal antirun of composite numbers differing by more than one.

%I A373404 #8 Jun 06 2024 23:57:36
%S A373404 18,9,36,15,54,21,46,25,26,27,90,33,34,35,74,39,126,45,94,49,50,51,
%T A373404 106,55,56,57,180,63,64,65,134,69,216,75,76,77,158,81,166,85,86,87,
%U A373404 178,91,92,93,94,95,194,99,306,105,324,111,226,115,116,117,118,119
%N A373404 Sum of the n-th maximal antirun of composite numbers differing by more than one.
%C A373404 The length of this antirun is given by A373403.
%C A373404 An antirun of a sequence (in this case A002808) is an interval of positions at which consecutive terms differ by more than one.
%H A373404 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373404 Row sums of:
%e A373404    4   6   8
%e A373404    9
%e A373404   10  12  14
%e A373404   15
%e A373404   16  18  20
%e A373404   21
%e A373404   22  24
%e A373404   25
%e A373404   26
%e A373404   27
%e A373404   28  30  32
%e A373404   33
%e A373404   34
%e A373404   35
%e A373404   36  38
%e A373404   39
%e A373404   40  42  44
%t A373404 Total/@Split[Select[Range[100],CompositeQ],#1+1!=#2&]//Most
%Y A373404 Partial sums are a subset of A053767 (partial sums of composite numbers).
%Y A373404 Functional neighbors: A005381, A054265, A068780, A373403, A373405, A373411, A373412.
%Y A373404 A000040 lists the primes, differences A001223.
%Y A373404 A002808 lists the composite numbers, differences A073783.
%Y A373404 A046933 counts composite numbers between primes.
%Y A373404 A065855 counts composite numbers up to n.
%Y A373404 Cf. A003114, A027833, A038664, A293697, A350842 (strict A350844), A371201.
%K A373404 nonn
%O A373404 1,1
%A A373404 _Gus Wiseman_, Jun 05 2024