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

1,1

Comments

Numbers whose digit sum is 2.

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

By extension, numbers k such that digitsum(k)^2 - 1 is prime. (PROOF: For any number k whose digit sum d > 2, d^2 - 1 = (d+1)*(d-1) and thus is not prime.) - Christian N. K. Anderson, Apr 22 2024

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)

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

Example

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)

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 *)

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
(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

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,changed

Author

Henry Bottomley, Feb 01 2000

Status

approved