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

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, 71, 73, 74, 79, 83, 86, 89, 97, 101, 103, 106, 107, 109, 113, 122, 127, 131, 137, 139, 142, 149, 151, 157, 158, 163, 167, 173, 178, 179, 181, 191, 193, 197, 199, 202

Offset

1,2

Comments

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.

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Links

Table of n, a(n) for n=1..60.

Formula

Consists of 1, the primes, and all odd-indexed primes times 2.

Mathematica

nn=1000;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
seq=Table[If[n==1, 1, 2*Median[prix[n]]], {n, nn}];
Select[Range[nn], FreeQ[seq[[Range[#-1]]], seq[[#]]]&]

Crossrefs

Positions of first appearances in A360005.

The unsorted version is A360006.

For mean instead of median we have A360008.

A112798 lists prime indices, length A001222, sum A056239.

A316413 lists numbers whose prime indices have integer mean.

A325347 = partitions w/ integer median, strict A359907, complement A307683.

A326567/A326568 gives mean of prime indices.

A359893 counts partitions by median, cf. A359901, A359902.

A359908 = numbers w/ integer median of prime indices, complement A359912.

Cf. A026424, A359889, A359890, A360009.

Sequence in context: A003172 A340856 A325100 * A053329 A308420 A363462

Adjacent sequences: A360004 A360005 A360006 * A360008 A360009 A360010

Keyword

nonn

Author

Gus Wiseman, Jan 24 2023

Status

approved