A061196 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.

0, 1, 2, 10, 3, 11, 100, 4, 12, 20, 101, 1000, 5, 13, 21, 102, 110, 1001, 10000, 6, 14, 22, 30, 103, 111, 200, 1002, 1010, 10001, 100000, 7, 15, 23, 31, 104, 112, 120, 201, 1003, 1011, 1100, 10002, 10010, 100001, 1000000, 8, 16, 24, 32, 40, 105, 113, 121, 202

Offset

0,3

Comments

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

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

Links

Andrew Howroyd, Table of n, a(n) for n = 0..96

Rasa Smidtaite and Minvydas Ragulskis, Commentary: Multidimensional discrete chaotic maps, Front. Phys. (2022) Vol. 10, 1094240.

Formula

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

Example

From Andrew Howroyd, Apr 25 2023: (Start)
The sequence as a triangle T(n,k) begins:
  0 | 0;
  1 | 1;
  2 | 2, 10;
  3 | 3, 11, 100;
  4 | 4, 12,  20, 101, 1000;
  5 | 5, 13,  21, 102,  110, 1001, 10000;
  6 | 6, 14,  22,  30,  103,  111,   200, 1002, 1010, 10001, 100000;
  ...
(End)

Mathematica

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 *)

Prog

(PARI)
F(p)={my(v=vector(if(#p, p[#p], 1))); for(i=1, #p, v[p[i]]++); v}
row(n)={my(R=[F(p) | p<-partitions(n)]); vecsort([fromdigits(Vecrev(u)) | u<-R, vecmax(u)<=9])}
{ for(n=0, 7, print(row(n))) } \\ Andrew Howroyd, Apr 25 2023

Crossrefs

Cf. A000041, A028897, A261776.

Sequence in context: A239083 A239084 A322000 * A239136 A239137 A252758

Adjacent sequences: A061193 A061194 A061195 * A061197 A061198 A061199

Keyword

nonn,base

Author

Henry Bottomley, Apr 20 2001

Status

approved