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