A038444 Sums of 2 distinct powers of 10.

11, 101, 110, 1001, 1010, 1100, 10001, 10010, 10100, 11000, 100001, 100010, 100100, 101000, 110000, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000, 100000001, 100000010, 100000100

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A052216 and of A007088.

Cf. A018900.

Programs

Haskell

a038444 n = a038444_list !! (n-1)
a038444_list = 11 : f [11] 90 where
   f xs@(x:_) z = ys ++ f ys (10 * z) where
                  ys = (x + z) : map (* 10) xs
-- Reinhard Zumkeller, Jan 28 2015

Maple

seq(seq(10^d + 10^j, j=0..d-1), d=1..10); # Robert Israel, Oct 14 2016

Mathematica

Sort[Total/@Subsets[10^Range[0,7],{2}]] (* Harvey P. Dale, Apr 20 2012 *)

PARI

a(n)= 10^(n-1-binomial(sqrtint(n*8)\/2, 2)) + 10^((sqrtint(n*8)+1)\2); \\ Ruud H.G. van Tol, Nov 29 2024

Python

from math import isqrt
def A038444(n): return 10**(m:=isqrt(n<<3)+1>>1)+10**(n-1-(m*(m-1)>>1)) # Chai Wah Wu, Mar 11 2025

Formula

G.f.: (10*x - 55*x^2 + Sum_{d>=1} (4*10^d+5)*x^((d^2-d)/2+1) - Sum_{d>=1} (445*10^(d-1)+5)*x^((d^2-d)/2+2))/(5*(1-x)*(1-10*x)). - Robert Israel, Oct 14 2016

Extensions

Offset corrected by Reinhard Zumkeller, Jan 28 2015