A052216 Sum 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

Offset

1,1

Comments

Numbers n such that sum of digits is 2.

A007953(a(n)) = 2; number of repdigits = #{2,11} = A242627(2) = 2. - Reinhard Zumkeller, Jul 17 2014

a(n) = 3*A237424(n) - 1. - Reinhard Zumkeller, Jan 28 2015

Links

Vincenzo Librandi, T. D. Noe and R. Zumkeller, Table of n, a(n) for n = 1..10000 (first 48 terms from V. Librandi, up to 1036 from T. D. Noe)

Formula

Sum of two powers of 10: a(n) = 10^n + 10^m for n >= 0, m = 0..n.

Example

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, etc.
- Bruno Berselli, Mar 07 2013

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 *)

Prog

(Magma) [n: n in [1..10100000] | &+Intseq(n) eq 2]; // Vincenzo Librandi, Mar 07 2013
(Magma) /* As a triangular array: */ [[10^n+10^m: m in [0..n]]: n in [0..8]]; // Bruno Berselli, Mar 07 2013
(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
(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
(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

Crossrefs

Subsequence of A069263 and A107679. A038444 is a subsequence.

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).

Cf. A007953, A242614, A242627, A237424.

Sequence in context: A115095 A341003 A061907 * A094629 A336034 A081242

Adjacent sequences: A052213 A052214 A052215 * A052217 A052218 A052219

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Feb 01 2000

Status

approved