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
KEYWORD
AUTHOR
Henry Bottomley, Feb 01 2000
STATUS
approved