cp's OEIS Frontend

A373821 Run-lengths of run-lengths of first differences of odd primes.

%I A373821 #7 Jun 22 2024 18:05:27
%S A373821 1,11,1,19,1,1,1,5,1,6,1,16,1,27,1,3,1,1,1,6,1,9,1,29,1,2,1,18,1,1,1,
%T A373821 5,1,3,1,17,1,19,1,30,1,17,1,46,1,17,1,27,1,30,1,5,1,36,1,41,1,10,1,
%U A373821 31,1,44,1,4,1,14,1,6,1,2,1,32,1,13,1,17,1,5
%N A373821 Run-lengths of run-lengths of first differences of odd primes.
%C A373821 Run-lengths of A333254.
%C A373821 The first term other than 1 at an odd positions is at a(101) = 2.
%C A373821 Also run-lengths (differing by 0) of run-lengths (differing by 0) of run-lengths (differing by 1) of composite numbers.
%e A373821 The odd primes are:
%e A373821 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
%e A373821 with first differences:
%e A373821 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, ...
%e A373821 with run-lengths:
%e A373821 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, ...
%e A373821 with run-lengths a(n).
%t A373821 Length/@Split[Length /@ Split[Differences[Select[Range[3,1000],PrimeQ]]]//Most]//Most
%Y A373821 Run-lengths of run-lengths of A046933(n) = A001223(n) - 1.
%Y A373821 Run-lengths of A333254.
%Y A373821 A000040 lists the primes.
%Y A373821 A001223 gives differences of consecutive primes.
%Y A373821 A027833 gives antirun lengths of odd primes (partial sums A029707).
%Y A373821 A065855 counts composite numbers up to n.
%Y A373821 A071148 gives partial sums of odd primes.
%Y A373821 A373820 gives run-lengths of antirun-lengths of odd primes.
%Y A373821 For prime runs: A001359, A006512, A025584, A067774, A373406.
%Y A373821 For composite runs: A005381, A008864, A054265, A176246, A251092, A373403.
%Y A373821 Cf. A006560, A037201, A038664, A069010, A373824, A373825.
%K A373821 nonn
%O A373821 1,2
%A A373821 _Gus Wiseman_, Jun 22 2024