A068743 - OEIS

%I #14 May 18 2024 15:19:50

%S 0,1,2,11,3,21,111,4,22,31,211,1111,5,32,41,221,311,2111,11111,6,33,

%T 42,51,222,321,411,2211,3111,21111,111111,7,43,52,61,322,331,421,511,

%U 2221,3211,4111,22111,31111,211111,1111111,8,44,53,62,71,332,422,431,521

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

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

%H Harvey P. Dale, <a href="/A068743/b068743.txt">Table of n, a(n) for n = 0..2500</a> [a(2088) corrected by Sean A. Irvine]

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%e 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.

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

%Y 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).

%K base,nonn

%O 0,3

%A _Henry Bottomley_, Feb 27 2002