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