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

Author

Henry Bottomley, Feb 27 2002

Keywords

• base
• nonn

Comments

a(97) cannot be written in decimal since it requires ten to be written as a single digit.

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

Cf. A060002 which writes the partitions with smallest digit first, number of values of a(n) with a digit sum of k is A000041, number of values of a(n) with a digit sum of k and m digits is A008284, a(A000070(n))=n+1 written as a single digit, a(A026905(n))=A000042(n).

Programs

Mathematica

Table[Sort[FromDigits[Flatten[IntegerDigits/@#]]&/@IntegerPartitions[n]],{n,0,20}]//Flatten (* Harvey P. Dale, May 18 2024 *)