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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.
5
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).
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
KEYWORD
nonn,tabf,base
AUTHOR
Rémy Sigrist, Mar 30 2022
STATUS
approved