cp's OEIS Frontend

A360007 Positions of first appearances in the sequence giving the median of the prime indices of n (A360005(n)/2).

%I A360007 #5 Jan 24 2023 12:35:41
%S A360007 1,2,3,5,6,7,11,13,14,17,19,23,26,29,31,37,38,41,43,47,53,58,59,61,67,
%T A360007 71,73,74,79,83,86,89,97,101,103,106,107,109,113,122,127,131,137,139,
%U A360007 142,149,151,157,158,163,167,173,178,179,181,191,193,197,199,202
%N A360007 Positions of first appearances in the sequence giving the median of the prime indices of n (A360005(n)/2).
%C A360007 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.
%C A360007 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%F A360007 Consists of 1, the primes, and all odd-indexed primes times 2.
%t A360007 nn=1000;
%t A360007 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360007 seq=Table[If[n==1,1,2*Median[prix[n]]],{n,nn}];
%t A360007 Select[Range[nn],FreeQ[seq[[Range[#-1]]],seq[[#]]]&]
%Y A360007 Positions of first appearances in A360005.
%Y A360007 The unsorted version is A360006.
%Y A360007 For mean instead of median we have A360008.
%Y A360007 A112798 lists prime indices, length A001222, sum A056239.
%Y A360007 A316413 lists numbers whose prime indices have integer mean.
%Y A360007 A325347 = partitions w/ integer median, strict A359907, complement A307683.
%Y A360007 A326567/A326568 gives mean of prime indices.
%Y A360007 A359893 counts partitions by median, cf. A359901, A359902.
%Y A360007 A359908 = numbers w/ integer median of prime indices, complement A359912.
%Y A360007 Cf. A026424, A359889, A359890, A360009.
%K A360007 nonn
%O A360007 1,2
%A A360007 _Gus Wiseman_, Jan 24 2023