A352724 - OEIS

%I #9 Apr 01 2022 09:02:15

%S 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 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 32,1,4,32,6,32,7,32,8,32,1,8,32,2,8,32,3,8,32

%N 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 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 Rémy Sigrist, <a href="/A352724/b352724.txt">Table of n, a(n) for n = 1..6145</a> (rows for n = 1..2048, flattened)

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

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

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

%e Irregular table begins:

%e      1:   [1]

%e      2:   [2]

%e      3:   [3]

%e      4:   [4]

%e      5:   [1, 4]

%e      6:   [6]

%e      7:   [7]

%e      8:   [8]

%e      9:   [1, 8]

%e     10:   [2, 8]

%e     11:   [3, 8]

%e     12:   [12]

%e     13:   [1, 12]

%e     14:   [14]

%e     15:   [15]

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

%K nonn,tabf,base

%O 1,2

%A _Rémy Sigrist_, Mar 30 2022