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A373826 Sorted positions of first appearances in the run-lengths (differing by 0) of the antirun-lengths (differing by > 2) of the odd primes.

%I A373826 #5 Jun 22 2024 22:08:54
%S A373826 1,4,38,6781,23238,26100
%N A373826 Sorted positions of first appearances in the run-lengths (differing by 0) of the antirun-lengths (differing by > 2) of the odd primes.
%C A373826 Sorted positions of first appearances in A373820 (run-lengths of A027833 with 1 prepended).
%e A373826 The odd primes begin:
%e A373826 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
%e A373826 with antiruns (differing by > 2):
%e A373826 (3), (5), (7,11), (13,17), (19,23,29), (31,37,41), (43,47,53,59), ...
%e A373826 with lengths:
%e A373826 1, 1, 2, 2, 3, 3, 4, 3, 6, 2, 5, 2, 6, 2, 2, 4, 3, 5, 3, 4, 5, 12, ...
%e A373826 which have runs:
%e A373826 (1,1), (2,2), (3,3), (4), (3), (6), (2), (5), (2), (6), (2,2), (4), ...
%e A373826 with lengths:
%e A373826 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A373826 with sorted positions of first appearances a(n).
%t A373826 t=Length/@Split[Length /@ Split[Select[Range[3,10000],PrimeQ],#1+2!=#2&]];
%t A373826 Select[Range[Length[t]],FreeQ[Take[t,#-1],t[[#]]]&]
%Y A373826 Sorted positions of first appearances in A373820, cf. A027833.
%Y A373826 For runs we have A373824 (unsorted A373825), sorted firsts of A373819.
%Y A373826 The unsorted version is A373827.
%Y A373826 A000040 lists the primes.
%Y A373826 A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.
%Y A373826 A046933 counts composite numbers between primes.
%Y A373826 A065855 counts composite numbers up to n.
%Y A373826 A071148 gives partial sums of odd primes.
%Y A373826 Cf. A001359, A006512, A025584, A037201, A038664, A054265, A067774, A176246, A251092, A373404, A373405, A373406.
%K A373826 nonn,more
%O A373826 1,2
%A A373826 _Gus Wiseman_, Jun 22 2024