A352724 Irregular table T(n, k) read by rows; the n-th row contains the lexicographically earlier list of A069010(n) distinct terms of A023758 summing to n.

1, 2, 3, 4, 1, 4, 6, 7, 8, 1, 8, 2, 8, 3, 8, 12, 1, 12, 14, 15, 16, 1, 16, 2, 16, 3, 16, 4, 16, 1, 4, 16, 6, 16, 7, 16, 24, 1, 24, 2, 24, 3, 24, 28, 1, 28, 30, 31, 32, 1, 32, 2, 32, 3, 32, 4, 32, 1, 4, 32, 6, 32, 7, 32, 8, 32, 1, 8, 32, 2, 8, 32, 3, 8, 32

Offset: 1

Author

Rémy Sigrist, Mar 30 2022

Keywords

• nonn
• tabf
• base

Comments

In other words, the n-th row gives the minimal partition of n into terms of A023758 (runs of consecutive 1's in binary).

Examples

			Irregular table begins:
     1:   [1]
     2:   [2]
     3:   [3]
     4:   [4]
     5:   [1, 4]
     6:   [6]
     7:   [7]
     8:   [8]
     9:   [1, 8]
    10:   [2, 8]
    11:   [3, 8]
    12:   [12]
    13:   [1, 12]
    14:   [14]
    15:   [15]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..6145 (rows for n = 1..2048, flattened)
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A023758, A069010 (row lengths), A133457, A342126, A342410.

Programs

PARI

row(n) = { my (r=[], o=0); while (n, my (v=valuation(n+n%2, 2)); if (n%2, r=concat(r, (2^v-1)*2^o)); o+=v; n\=2^v); r }

Formula

Sum_{k = 1..A069010(n)} T(n, k) = n.

T(n, 1) = A342410(n).

T(n, A069010(n)) = A342126(n).