%I #53 Nov 03 2023 10:23:36

%S 3,12,21,30,102,111,120,201,210,300,1002,1011,1020,1101,1110,1200,

%T 2001,2010,2100,3000,10002,10011,10020,10101,10110,10200,11001,11010,

%U 11100,12000,20001,20010,20100,21000,30000,100002,100011,100020,100101

%N Numbers whose sum of digits is 3.

%C From _Joshua S.M. Weiner_, Oct 19 2012: (Start)

%C Sequence is a representation of the "energy states" of "multiplex" notation of 3 quantum of objects in a juggling pattern.

%C 0 = an empty site, or empty hand. 1 = one object resides in the site. 2 = two objects reside in the site. 3 = three objects reside in the site. (See A038447.) (End)

%C A007953(a(n)) = 3; number of repdigits = #{3,111} = A242627(3) = 2. - _Reinhard Zumkeller_, Jul 17 2014

%C Can be seen as a table whose n-th row holds the n-digit terms {10^(n-1) + 10^m + 10^k, 0 <= k <= m < n}, n >= 1. Row lengths are then (1, 3, 6, 10, ...) = n*(n+1)/2 = A000217(n). The first and the n last terms of row n are 10^(n-1) + 2 resp. 2*10^(n-1) + 10^k, 0 <= k < n. - _M. F. Hasler_, Feb 19 2020

%H Alois P. Heinz, <a href="/A052217/b052217.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..84 from Vincenzo Librandi, terms 85..1140 from T. D. Noe)

%F T(n,k) = 10^(n-1) + 10^A003056(k) + 10^A002262(k) when read as a table with row lengths n*(n+1)/2, n >= 1, 0 <= k < n*(n+1)/2. - _M. F. Hasler_, Feb 19 2020

%F a(n) = 10^A056556(n-1) + 10^A056557(n-1) + 10^A056558(n-1). - _Kevin Ryde_, Apr 17 2021

%t Union[FromDigits/@Select[Flatten[Table[Tuples[Range[0,3],n],{n,6}],1],Total[#]==3&]] (* _Harvey P. Dale_, Oct 20 2012 *)

%t Select[Range[10^6], Total[IntegerDigits[#]] == 3 &] (* _Vincenzo Librandi_, Mar 07 2013 *)

%t Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 18]], {s, IntegerPartitions[3]}]]] (* _T. D. Noe_, Mar 08 2013 *)

%o (Magma) [n: n in [1..100101] | &+Intseq(n) eq 3 ]; // _Vincenzo Librandi_, Mar 07 2013

%o (Haskell)

%o a052217 n = a052217_list !! (n-1)

%o a052217_list = filter ((== 3) . a007953) [0..]

%o -- _Reinhard Zumkeller_, Jul 17 2014

%o (PARI) isok(n) = sumdigits(n) == 3; \\ _Michel Marcus_, Dec 28 2015

%o (PARI) apply( {A052217_row(n,s,t=-1)=vector(n*(n+1)\2,k,t++>s&&t=!s++;10^(n-1)+10^s+10^t)}, [1..5]) \\ _M. F. Hasler_, Feb 19 2020

%o (Python)

%o from itertools import count, islice

%o def agen(): yield from (10**i + 10**j + 10**k for i in count(0) for j in range(i+1) for k in range(j+1))

%o print(list(islice(agen(), 40))) # _Michael S. Branicky_, May 14 2022

%Y Cf. A069521 to A069530, A069532 to A069537.

%Y Cf. A007953, A218043 (subsequence).

%Y Row n=3 of A245062.

%Y Other digit sums: A011557 (1), A052216 (2), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

%Y Other bases: A014311 (binary), A226636 (ternary), A179243 (Zeckendorf).

%Y Cf. A242614, A242627.

%Y Cf. A003056, A002262 (triangular coordinates), A056556, A056557, A056558 (tetrahedral coordinates).

%K base,easy,nonn

%O 1,1

%A _Henry Bottomley_, Feb 01 2000

%E Offset changed from 0 to 1 by _Vincenzo Librandi_, Mar 07 2013