cp's OEIS Frontend

A373824 Sorted positions of first appearances in the run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

%I A373824 #6 Jun 22 2024 22:09:03
%S A373824 1,2,11,13,29,33,45,51,57,59,69,75,105,129,211,227,301,313,321,341,
%T A373824 407,413,447,459,537,679,709,767,1113,1301,1405,1411,1429,1439,1709,
%U A373824 1829,1923,2491,2543,2791,2865,3301,3471,3641,4199,4611,5181,5231,6345,6555
%N A373824 Sorted positions of first appearances in the run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.
%C A373824 Sorted positions of first appearances in A373819.
%e A373824 The runs of odd primes differing by 2 begin:
%e A373824    3   5   7
%e A373824   11  13
%e A373824   17  19
%e A373824   23
%e A373824   29  31
%e A373824   37
%e A373824   41  43
%e A373824   47
%e A373824   53
%e A373824   59  61
%e A373824   67
%e A373824   71  73
%e A373824   79
%e A373824 with lengths:
%e A373824 3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, ...
%e A373824 which have runs beginning:
%e A373824   3
%e A373824   2 2
%e A373824   1
%e A373824   2
%e A373824   1
%e A373824   2
%e A373824   1 1
%e A373824   2
%e A373824   1
%e A373824   2
%e A373824   1 1 1 1
%e A373824   2 2
%e A373824   1 1 1
%e A373824 with lengths:
%e A373824 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 3, 2, 4, 3,...
%e A373824 with sorted positions of first appearances a(n).
%t A373824 t=Length/@Split[Length/@Split[Select[Range[3,10000],PrimeQ],#1+2==#2&]];
%t A373824 Select[Range[Length[t]],FreeQ[Take[t,#-1],t[[#]]]&]
%Y A373824 Sorted firsts of A373819 (run-lengths of A251092).
%Y A373824 The unsorted version is A373825.
%Y A373824 For antiruns we have A373826, unsorted A373827.
%Y A373824 A000040 lists the primes.
%Y A373824 A001223 gives differences of consecutive primes (firsts A073051), run-lengths A333254 (firsts A335406), run-lengths of run-lengths A373821.
%Y A373824 A046933 counts composite numbers between primes.
%Y A373824 A065855 counts composite numbers up to n.
%Y A373824 A071148 gives partial sums of odd primes.
%Y A373824 A373820 gives run-lengths of antirun-lengths, run-lengths of A027833.
%Y A373824 For prime runs: A001359, A006512, A025584, A067774, A373405, A373406.
%Y A373824 For composite runs: A005381, A054265, A068780, A373403, A373404.
%Y A373824 Cf. A006560, A006562, A029707, A037201, A038664, A069010, A122535, A176246, A373401, A373402.
%K A373824 nonn
%O A373824 1,2
%A A373824 _Gus Wiseman_, Jun 21 2024