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A373820 Run-lengths (differing by 0) of antirun-lengths (differing by > 2) of odd primes.

%I A373820 #5 Jun 22 2024 18:05:35
%S A373820 2,2,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,
%T A373820 1,1,1,3,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A373820 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,3,1,1,1
%N A373820 Run-lengths (differing by 0) of antirun-lengths (differing by > 2) of odd primes.
%C A373820 Run-lengths of the version of A027833 with 1 prepended.
%H A373820 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373820 The antiruns of odd primes (differing by > 2) begin:
%e A373820    3
%e A373820    5
%e A373820    7  11
%e A373820   13  17
%e A373820   19  23  29
%e A373820   31  37  41
%e A373820   43  47  53  59
%e A373820   61  67  71
%e A373820   73  79  83  89  97 101
%e A373820  103 107
%e A373820  109 113 127 131 137
%e A373820  139 149
%e A373820  151 157 163 167 173 179
%e A373820  181 191
%e A373820  193 197
%e A373820  199 211 223 227
%e A373820  229 233 239
%e A373820  241 251 257 263 269
%e A373820  271 277 281
%e A373820 with lengths:
%e A373820 1, 1, 2, 2, 3, 3, 4, 3, 6, 2, 5, 2, 6, 2, 2, ...
%e A373820 with runs:
%e A373820   1  1
%e A373820   2  2
%e A373820   3  3
%e A373820   4
%e A373820   3
%e A373820   6
%e A373820   2
%e A373820   5
%e A373820   2
%e A373820   6
%e A373820   2  2
%e A373820   4
%e A373820   3
%e A373820   5
%e A373820   3
%e A373820   4
%e A373820 with lengths a(n).
%t A373820 Length/@Split[Length/@Split[Select[Range[3,1000],PrimeQ],#2-#1>2&]//Most]//Most
%Y A373820 Run-lengths of A027833 (if we prepend 1), partial sums A029707.
%Y A373820 For runs we have A373819, run-lengths of A251092.
%Y A373820 Positions of first appearances are A373827, sorted A373826.
%Y A373820 A000040 lists the primes.
%Y A373820 A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.
%Y A373820 A046933 counts composite numbers between primes.
%Y A373820 A065855 counts composite numbers up to n.
%Y A373820 A071148 gives partial sums of odd primes.
%Y A373820 For prime runs: A001359, A006512, A025584, A067774, A373405, A373406.
%Y A373820 For composite runs: A005381, A054265, A068780, A373403, A373404.
%Y A373820 Cf. A005117, A006560, A006562, A037201, A038664, A049579, A073051, A076259, A122535, A176246.
%K A373820 nonn
%O A373820 1,1
%A A373820 _Gus Wiseman_, Jun 22 2024