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

1,2

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).

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

Formula

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

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

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

Example

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]

Prog

(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 }

Crossrefs

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

Sequence in context: A129717 A317088 A276380 * A248723 A117742 A117716

Adjacent sequences: A352721 A352722 A352723 * A352725 A352726 A352727

Keyword

nonn,tabf,base

Author

Rémy Sigrist, Mar 30 2022

Status

approved