cp's OEIS Frontend

A373405 Sum of the n-th maximal antirun of odd primes differing by more than two.

%I A373405 #7 Jun 07 2024 00:18:09
%S A373405 3,5,18,30,71,109,202,199,522,210,617,288,990,372,390,860,701,1281,
%T A373405 829,1194,1645,4578,852,2682,4419,3300,2927,2438,1891,2602,14660,1632,
%U A373405 1650,3378,3480,18141,2052,3121,2112,4310,8922,13131,6253,3851,3889,3929,13788
%N A373405 Sum of the n-th maximal antirun of odd primes differing by more than two.
%C A373405 The length of this run is given by A027833 (except initial term).
%C A373405 An antirun of a sequence (in this case A000040\{2}) is an interval of positions at which consecutive terms differ by more than one.
%H A373405 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373405 Row-sums of:
%e A373405    3
%e A373405    5
%e A373405    7  11
%e A373405   13  17
%e A373405   19  23  29
%e A373405   31  37  41
%e A373405   43  47  53  59
%e A373405   61  67  71
%e A373405   73  79  83  89  97 101
%t A373405 Total/@Split[Select[Range[3,1000],PrimeQ],#1+2!=#2&]//Most
%Y A373405 The partial sums are a subset of A071148 (partial sums of odd primes).
%Y A373405 Functional neighbors: A001359, A006512, A027833 (partial sums A029707), A373404, A373406, A373411, A373412.
%Y A373405 A000040 lists the primes, differences A001223.
%Y A373405 A002808 lists the composite numbers, differences A073783.
%Y A373405 Cf. A025157, A038664, A046933, A293697, A350842 (strict A350844), A371201.
%K A373405 nonn
%O A373405 1,1
%A A373405 _Gus Wiseman_, Jun 05 2024