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%I #51 Feb 22 2024 16:01:10
%S 2,11,20,101,110,200,1001,1010,1100,2000,10001,10010,10100,11000,
%T 20000,100001,100010,100100,101000,110000,200000,1000001,1000010,
%U 1000100,1001000,1010000,1100000,2000000,10000001,10000010,10000100,10001000,10010000,10100000,11000000,20000000
%N Sums of two powers of 10.
%C Numbers whose digit sum is 2.
%C A007953(a(n)) = 2; number of repdigits = #{2,11} = A242627(2) = 2. - _Reinhard Zumkeller_, Jul 17 2014
%H Reinhard Zumkeller, <a href="/A052216/b052216.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..48 from Vincenzo Librandi, terms 49..1036 from T. D. Noe)
%F T(n,k) = 10^(n-1) + 10^(k-1) with 1 <= k <= n.
%F a(n) = 3*A237424(n) - 1. - _Reinhard Zumkeller_, Jan 28 2015
%e From _Bruno Berselli_, Mar 07 2013: (Start)
%e The triangular array starts (see formula):
%e 2;
%e 11, 20;
%e 101, 110, 200;
%e 1001, 1010, 1100, 2000;
%e 10001, 10010, 10100, 11000, 20000;
%e 100001, 100010, 100100, 101000, 110000, 200000;
%e 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000;
%e ...
%e (End)
%t t = 10^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* _T. D. Noe_, Oct 09 2011 *)
%t With[{nn=7},Sort[Join[Table[FromDigits[PadRight[{2},n,0]],{n,nn}], FromDigits/@Flatten[Table[Table[Insert[PadRight[{1},n,0],1,i]],{n,nn},{i,2,n+1}],1]]]] (* _Harvey P. Dale_, Nov 15 2011 *)
%t Select[Range[10^9], Total[IntegerDigits[#]] == 2&] (* _Vincenzo Librandi_, Mar 07 2013 *)
%t T[n_,k_]:=10^(n-1)+10^(k-1); Table[T[n,k],{n,8},{k,n}]//Flatten (* _Stefano Spezia_, Nov 03 2023 *)
%o (Magma) [n: n in [1..10100000] | &+Intseq(n) eq 2]; // _Vincenzo Librandi_, Mar 07 2013
%o (Magma) /* As a triangular array: */ [[10^n+10^m: m in [0..n]]: n in [0..8]]; // _Bruno Berselli_, Mar 07 2013
%o (Haskell)
%o a052216 n = a052216_list !! (n-1)
%o a052216_list = 2 : f [2] 9 where
%o f xs@(x:_) z = ys ++ f ys (10 * z) where
%o ys = (x + z) : map (* 10) xs
%o -- _Reinhard Zumkeller_, Jan 28 2015, Jul 17 2014
%o (PARI) a(n)=my(d=(sqrtint(8*n)-1)\2,t=n-d*(d+1)/2-1); 10^d + 10^t \\ _Charles R Greathouse IV_, Dec 19 2016
%o (Python)
%o from itertools import count, islice
%o def agen(): yield from (10**i + 10**j for i in count(0) for j in range(i+1))
%o print(list(islice(agen(), 34))) # _Michael S. Branicky_, May 15 2022
%o (SageMath)
%o def A052216(n,k): return 10^(n-1) + 10^(k-1)
%o flatten([[A052216(n,k) for k in range(1,n+1)] for n in range(1,13)]) # _G. C. Greubel_, Feb 22 2024
%Y Subsequence of A069263 and A107679. A038444 is a subsequence.
%Y Sums of n powers of 10: A011557 (1), A052217 (3), 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 Cf. A007953, A242614, A242627, A237424.
%K easy,nonn,tabl
%O 1,1
%A _Henry Bottomley_, Feb 01 2000
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