cp's OEIS Frontend

A373827 Position of first appearance of n in the run-lengths (differing by 0) of the antirun-lengths (differing by > 2) of the odd primes.

%I A373827 #5 Jun 22 2024 22:08:50
%S A373827 4,1,38,6781,26100,23238
%N A373827 Position of first appearance of n in the run-lengths (differing by 0) of the antirun-lengths (differing by > 2) of the odd primes.
%C A373827 Positions of first appearances in A373820 (run-lengths of A027833 with 1 prepended).
%e A373827 The odd primes begin:
%e A373827 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
%e A373827 with antiruns (differing by > 2):
%e A373827 (3), (5), (7,11), (13,17), (19,23,29), (31,37,41), (43,47,53,59), ...
%e A373827 with lengths:
%e A373827 1, 1, 2, 2, 3, 3, 4, 3, 6, 2, 5, 2, 6, 2, 2, 4, 3, 5, 3, 4, 5, 12, ...
%e A373827 which have runs:
%e A373827 (1,1), (2,2), (3,3), (4), (3), (6), (2), (5), (2), (6), (2,2), (4), ...
%e A373827 with lengths:
%e A373827 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A373827 with positions of first appearances a(n).
%t A373827 t=Length/@Split[Length /@ Split[Select[Range[3,10000],PrimeQ],#1+2!=#2&]//Most]//Most;
%t A373827 spna[y_]:=Max@@Select[Range[Length[y]],SubsetQ[t,Range[#1]]&];
%t A373827 Table[Position[t,k][[1,1]],{k,spna[t]}]
%Y A373827 Positions of first appearances in A373820.
%Y A373827 For runs instead of antiruns we have A373825, sorted A373824.
%Y A373827 The sorted version is A373826.
%Y A373827 A000040 lists the primes.
%Y A373827 A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.
%Y A373827 A046933 counts composite numbers between primes.
%Y A373827 A065855 counts composite numbers up to n.
%Y A373827 A071148 gives partial sums of odd primes.
%Y A373827 Cf. A001359, A006512, A025584, A027833, A037201, A038664, A054265, A067774, A176246, A251092, A373404, A373405, A373406.
%K A373827 nonn,more
%O A373827 1,1
%A A373827 _Gus Wiseman_, Jun 22 2024