cp's OEIS Frontend

A360555 Two times the median of the first differences of the 0-prepended prime indices of n > 1.

%I A360555 #5 Feb 15 2023 21:48:27
%S A360555 2,4,1,6,2,8,0,2,3,10,2,12,4,3,0,14,2,16,2,4,5,18,1,3,6,0,2,20,2,22,0,
%T A360555 5,7,4,1,24,8,6,1,26,2,28,2,2,9,30,0,4,2,7,2,32,1,5,1,8,10,34,2,36,11,
%U A360555 4,0,6,2,38,2,9,2,40,0,42,12,2,2,5,2,44,0,0
%N A360555 Two times the median of the first differences of the 0-prepended prime indices of n > 1.
%C A360555 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length). Since the denominator is always 1 or 2, the median can be represented as an integer by multiplying by 2.
%C A360555 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A360555 The 0-prepended prime indices of 1617 are {0,2,4,4,5}, with sorted differences {0,1,2,2}, with median 3/2, so a(1617) = 3.
%t A360555 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360555 Table[2*Median[Differences[Prepend[prix[n],0]]],{n,2,100}]
%Y A360555 The version for divisors is A063655.
%Y A360555 Differences of 0-prepended prime indices are listed by A287352.
%Y A360555 The version for prime indices is A360005.
%Y A360555 The version for distinct prime indices is A360457.
%Y A360555 The version for distinct prime factors is A360458.
%Y A360555 The version for prime factors is A360459.
%Y A360555 The version for prime multiplicities is A360460.
%Y A360555 Positions of even terms are A360556
%Y A360555 Positions of odd terms are A360557
%Y A360555 Positions of 0's are A360558, counted by A360254.
%Y A360555 For mean instead of two times median we have A360614/A360615.
%Y A360555 A112798 lists prime indices, length A001222, sum A056239.
%Y A360555 A325347 counts partitions with integer median, complement A307683.
%Y A360555 A326567/A326568 gives mean of prime indices.
%Y A360555 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360555 Cf. A000975, A026424, A359907, A359908, A359912, A360550.
%K A360555 nonn
%O A360555 2,1
%A A360555 _Gus Wiseman_, Feb 14 2023