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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.

%I A352724 #9 Apr 01 2022 09:02:15
%S A352724 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,
%T A352724 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,
%U A352724 32,1,4,32,6,32,7,32,8,32,1,8,32,2,8,32,3,8,32
%N 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.
%C A352724 In other words, the n-th row gives the minimal partition of n into terms of A023758 (runs of consecutive 1's in binary).
%H A352724 Rémy Sigrist, <a href="/A352724/b352724.txt">Table of n, a(n) for n = 1..6145</a> (rows for n = 1..2048, flattened)
%H A352724 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A352724 Sum_{k = 1..A069010(n)} T(n, k) = n.
%F A352724 T(n, 1) = A342410(n).
%F A352724 T(n, A069010(n)) = A342126(n).
%e A352724 Irregular table begins:
%e A352724      1:   [1]
%e A352724      2:   [2]
%e A352724      3:   [3]
%e A352724      4:   [4]
%e A352724      5:   [1, 4]
%e A352724      6:   [6]
%e A352724      7:   [7]
%e A352724      8:   [8]
%e A352724      9:   [1, 8]
%e A352724     10:   [2, 8]
%e A352724     11:   [3, 8]
%e A352724     12:   [12]
%e A352724     13:   [1, 12]
%e A352724     14:   [14]
%e A352724     15:   [15]
%o A352724 (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 }
%Y A352724 Cf. A023758, A069010 (row lengths), A133457, A342126, A342410.
%K A352724 nonn,tabf,base
%O A352724 1,2
%A A352724 _Rémy Sigrist_, Mar 30 2022