

A068743


Digitized partition numbers: numbers with (weakly) decreasing digits ordered by sum of their digits then by the numbers themselves.


2



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
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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



