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A373819 Run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

%I A373819 #9 Jun 22 2024 14:08:57
%S A373819 1,2,1,1,1,1,2,1,1,1,4,2,3,2,4,3,2,1,1,1,3,1,1,1,2,1,3,1,10,2,4,1,7,1,
%T A373819 4,1,3,1,2,1,1,1,2,1,18,3,2,1,2,1,17,2,1,2,2,1,6,1,9,1,3,1,1,1,1,1,1,
%U A373819 1,8,1,3,1,2,2,15,1,1,1,4,1,1,1,1,1,7,1
%N A373819 Run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.
%C A373819 Run-lengths of A251092.
%H A373819 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373819 The odd primes begin:
%e A373819 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
%e A373819 with runs:
%e A373819    3   5   7
%e A373819   11  13
%e A373819   17  19
%e A373819   23
%e A373819   29  31
%e A373819   37
%e A373819   41  43
%e A373819   47
%e A373819   53
%e A373819   59  61
%e A373819   67
%e A373819   71  73
%e A373819 with lengths:
%e A373819 3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, ...
%e A373819 which have runs beginning:
%e A373819   3
%e A373819   2 2
%e A373819   1
%e A373819   2
%e A373819   1
%e A373819   2
%e A373819   1 1
%e A373819   2
%e A373819   1
%e A373819   2
%e A373819   1 1 1 1
%e A373819   2 2
%e A373819   1 1 1
%e A373819 with lengths a(n).
%t A373819 Length/@Split[Length/@Split[Select[Range[3,1000], PrimeQ],#1+2==#2&]//Most]//Most
%Y A373819 Run-lengths of A251092.
%Y A373819 For antiruns we have A373820, run-lengths of A027833 (if we prepend 1).
%Y A373819 Positions of first appearances are A373825, sorted A373824.
%Y A373819 A000040 lists the primes.
%Y A373819 A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.
%Y A373819 A046933 counts composite numbers between primes.
%Y A373819 A065855 counts composite numbers up to n.
%Y A373819 A071148 gives partial sums of odd primes.
%Y A373819 For prime runs: A001359, A006512, A025584, A067774, A373405, A373406.
%Y A373819 For composite runs: A005381, A054265, A068780, A373403, A373404.
%Y A373819 Cf. A005117, A006560, A006562, A029707, A037201, A038664, A076259, A176246.
%K A373819 nonn
%O A373819 1,2
%A A373819 _Gus Wiseman_, Jun 20 2024