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

1,1

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

Subsequence of A052216 and of A007088.

Cf. A018900.

Sequence in context: A043494 A277959 A278937 * A115824 A364326 A208259

Adjacent sequences: A038441 A038442 A038443 * A038445 A038446 A038447

Keyword

nonn,easy,changed

Author

Olivier Gérard

Extensions

Offset corrected by Reinhard Zumkeller, Jan 28 2015

Status

approved