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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.
1
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
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
KEYWORD
nonn,base
AUTHOR
Henry Bottomley, Apr 20 2001
STATUS
approved