A324081 -id:A324081 - cp's OEIS frontend

A324078 a(0) = 1, followed by pairs (value of rarest term, multiplicity of that value). Choose the least value of rarest term if there is a tie.

1, 1, 1, 1, 3, 3, 1, 3, 2, 2, 1, 2, 2, 3, 3, 2, 4, 4, 1, 4, 2, 4, 3, 4, 4, 2, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 6, 6, 5, 7, 7, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 7, 7, 3, 9, 9, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9, 8, 8, 1, 8, 2, 8, 3, 8, 4, 8, 5, 8, 6, 8, 7, 8, 8, 9, 9, 8, 10, 10, 1, 10, 2, 10, 3, 10

Offset: 0

Joerg Arndt, Feb 15 2019

nonn

			1, term 1 appears 1 time, term 1 appears 3 times, term 3 appears 1 time, term 3 appears 2 times, term 2 appears 1 time, ...

Joerg Arndt, Table of n, a(n) for n = 0..10000

A324079 is the same sequence with pairs after a(0) swapped.

A324080 is the sequence of rarest values, A324081 gives their multiplicities.

Nest[Append[#, First@ SortBy[Union@ Tally[Flatten@ #], Last]] &, {{1}}, 55] // Flatten (* Michael De Vlieger, Feb 25 2019 *)

A324080 a(n) is the rarest values appearing recorded in n-th pair in A324078.

Original entry on oeis.org

1, 1, 3, 3, 2, 2, 3, 2, 4, 4, 4, 4, 2, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 6, 5, 7, 7, 7, 7, 7, 7, 7, 3, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 5

Offset: 1

Joerg Arndt, Feb 15 2019

nonn

Dropping all but the first occurrence of the terms appears to give A080782.

Joerg Arndt, Table of n, a(n) for n = 1..5000

See A324081 for the multiplicities.

a(n) = A324078(2*n-1).

a(n) = A324079(2*n).

cp's OEIS Frontend

A324078 a(0) = 1, followed by pairs (value of rarest term, multiplicity of that value). Choose the least value of rarest term if there is a tie.

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