%I #25 Jun 03 2023 10:18:06

%S 0,1,2,10,3,11,100,4,12,20,101,1000,5,13,21,102,110,1001,10000,6,14,

%T 22,30,103,111,200,1002,1010,10001,100000,7,15,23,31,104,112,120,201,

%U 1003,1011,1100,10002,10010,100001,1000000,8,16,24,32,40,105,113,121,202

%N If n = Sum_{i} c_i * 10^i then let b(n) = Sum_{i} c_i * (i+1). Order the integers by b(n) and then n.

%C This is in effect a listing of single-digit (nonnegative) solutions to b + 2c + 3d + 4e + ... = k.

%C The sequence can be considered as an irregular triangle listing partitions in which no part occurs more than 9 times. The row lengths are given by A261776. For example, in row 5 the value 102, corresponds to the partition 1+1+3 (= 2*1 + 0*2 + 1*3). - _Andrew Howroyd_, Apr 25 2023

%H Andrew Howroyd, <a href="/A061196/b061196.txt">Table of n, a(n) for n = 0..96</a>

%H Rasa Smidtaite and Minvydas Ragulskis, <a href="https://doi.org/10.3389/fphy.2022.1094240">Commentary: Multidimensional discrete chaotic maps</a>, Front. Phys. (2022) Vol. 10, 1094240.

%F For n < 10, a(A000070(n)) = n+1 and a(A026905(n)) = 10^(n-1).

%e From _Andrew Howroyd_, Apr 25 2023: (Start)

%e The sequence as a triangle T(n,k) begins:

%e 0 | 0;

%e 1 | 1;

%e 2 | 2, 10;

%e 3 | 3, 11, 100;

%e 4 | 4, 12, 20, 101, 1000;

%e 5 | 5, 13, 21, 102, 110, 1001, 10000;

%e 6 | 6, 14, 22, 30, 103, 111, 200, 1002, 1010, 10001, 100000;

%e ...

%e (End)

%t With[{k = 7}, {{0}}~Join~Values@ PositionIndex[Array[Total@ MapIndexed[#1*First[#2] &, Reverse@ IntegerDigits[#]] &, 10^k]][[1 ;; k]]] // Flatten (* _Michael De Vlieger_, Dec 22 2022, solution only suitable for generating the data field *)

%o (PARI)

%o F(p)={my(v=vector(if(#p, p[#p], 1))); for(i=1, #p, v[p[i]]++); v}

%o row(n)={my(R=[F(p) | p<-partitions(n)]); vecsort([fromdigits(Vecrev(u)) | u<-R, vecmax(u)<=9])}

%o { for(n=0, 7, print(row(n))) } \\ _Andrew Howroyd_, Apr 25 2023

%Y Cf. A000041, A028897, A261776.

%K nonn,base

%O 0,3

%A _Henry Bottomley_, Apr 20 2001