A052216 Sums of two powers of 10.
2, 11, 20, 101, 110, 200, 1001, 1010, 1100, 2000, 10001, 10010, 10100, 11000, 20000, 100001, 100010, 100100, 101000, 110000, 200000, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000, 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000, 20000000
Offset: 1
Examples
From _Bruno Berselli_, Mar 07 2013: (Start)
The triangular array starts (see formula):
2;
11, 20;
101, 110, 200;
1001, 1010, 1100, 2000;
10001, 10010, 10100, 11000, 20000;
100001, 100010, 100100, 101000, 110000, 200000;
1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000;
...
(End)
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (terms 1..48 from Vincenzo Librandi, terms 49..1036 from T. D. Noe)
Crossrefs
Programs
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Haskell
a052216 n = a052216_list !! (n-1) a052216_list = 2 : f [2] 9 where f xs@(x:_) z = ys ++ f ys (10 * z) where ys = (x + z) : map (* 10) xs -- Reinhard Zumkeller, Jan 28 2015, Jul 17 2014 -
Magma
[n: n in [1..10100000] | &+Intseq(n) eq 2]; // Vincenzo Librandi, Mar 07 2013
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Magma
/* As a triangular array: */ [[10^n+10^m: m in [0..n]]: n in [0..8]]; // Bruno Berselli, Mar 07 2013
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Mathematica
t = 10^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *) 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 *) Select[Range[10^9], Total[IntegerDigits[#]] == 2&] (* Vincenzo Librandi, Mar 07 2013 *) T[n_,k_]:=10^(n-1)+10^(k-1); Table[T[n,k],{n,8},{k,n}]//Flatten (* Stefano Spezia, Nov 03 2023 *) -
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
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Python
from itertools import count, islice def agen(): yield from (10**i + 10**j for i in count(0) for j in range(i+1)) print(list(islice(agen(), 34))) # Michael S. Branicky, May 15 2022
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Python
from math import isqrt def A052216(n): return 10**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+10**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 08 2025
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SageMath
def A052216(n,k): return 10^(n-1) + 10^(k-1) flatten([[A052216(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Feb 22 2024
Formula
T(n,k) = 10^(n-1) + 10^(k-1) with 1 <= k <= n.
a(n) = 3*A237424(n) - 1. - Reinhard Zumkeller, Jan 28 2015
Comments