A068743 Digitized partition numbers: numbers with (weakly) decreasing digits ordered by sum of their digits then by the numbers themselves.
0, 1, 2, 11, 3, 21, 111, 4, 22, 31, 211, 1111, 5, 32, 41, 221, 311, 2111, 11111, 6, 33, 42, 51, 222, 321, 411, 2211, 3111, 21111, 111111, 7, 43, 52, 61, 322, 331, 421, 511, 2221, 3211, 4111, 22111, 31111, 211111, 1111111, 8, 44, 53, 62, 71, 332, 422, 431, 521
Offset: 0
Examples
The partitions of 6 are 6, 5+1, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1; removing the + signs gives 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111; ordering these by size gives 6, 33, 42, 51, 222, 321, 411, 2211, 3111, 21111, 111111 as part of the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..2500 [a(2088) corrected by Sean A. Irvine]
- Index entries for sequences related to partitions
Crossrefs
Programs
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Mathematica
Table[Sort[FromDigits[Flatten[IntegerDigits/@#]]&/@IntegerPartitions[n]],{n,0,20}]//Flatten (* Harvey P. Dale, May 18 2024 *)
Comments