A175025 -id:A175025 - cp's OEIS frontend

A175022 a(n) = the number of runs (those of 0 and of 1 considered together) in the binary representation of A175020(n).

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

Offset: 1

Leroy Quet, Nov 03 2009

a(n) gives the number of terms in row n of irregular tables A175023 and A175024.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A175020, A175023, A175024, A175025.

With[{s = Array[Sort@ Map[Length, Split@ IntegerDigits[#, 2]] &, 265]}, Map[Length@ Split@ IntegerDigits[#, 2] &, Values[PositionIndex@ s][[All, 1]] ]] (* Michael De Vlieger, Sep 03 2017 *)

Extended by Ray Chandler, Mar 11 2010

A175024 Irregular table read by rows: Row n (of A175022(n) terms) contains the terms of row n of table A175023 with these terms arranged in nondecreasing order.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 2, 4, 1, 4, 1, 1, 3, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 3, 5, 1, 5, 1, 1, 4, 1, 1, 1, 3, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 4, 2, 2, 2, 3, 3, 6, 1, 6, 1, 1, 5, 1, 1, 1, 4, 1, 2, 4, 1, 1, 2, 3, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 1, 2

Offset: 1

Leroy Quet, Nov 03 2009

This table lists the parts of the partitions of the positive integers. Each partition is represented exactly once in this table. If n is such that 2^(m-1) <= A175020(n) <= 2^m -1, then row n of this table gives one partition of m.

			Table to start:
1
1,1
2
1,2
1,1,1
3
1,3
1,1,2
1,1,1,1
2,2
4
1,4
1,1,3
1,1,1,2
1,2,2
1,1,1,1,1
2,3
5
Note there are: 1 row that sums to 1, two rows that sum to 2, three rows that sum to 3, five rows that sum to 4, seven rows that sum to 5, etc, where 1,2,3,5,7,... are the number of unrestricted partitions of 1,2,3,4,5,...

Cf. A175020, A175022, A175023, A175025.

Extended by Ray Chandler, Mar 11 2010

cp's OEIS Frontend

A175022 a(n) = the number of runs (those of 0 and of 1 considered together) in the binary representation of A175020(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions