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

0,3

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..2500

Index entries for sequences related to partitions

Example

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.

Mathematica

Table[Sort[FromDigits/@IntegerPartitions[n]], {n, 0, 10}]//Flatten (* Harvey P. Dale, Jul 05 2019 *)

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).

Sequence in context: A090323 A127668 A261300 * A322761 A113736 A241596

Adjacent sequences: A068740 A068741 A068742 * A068744 A068745 A068746

Keyword

base,nonn

Author

Henry Bottomley, Feb 27 2002

Status

approved