cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A038444 Sums of 2 distinct powers of 10.

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%I A038444 #29 Mar 11 2025 09:52:52
%S A038444 11,101,110,1001,1010,1100,10001,10010,10100,11000,100001,100010,
%T A038444 100100,101000,110000,1000001,1000010,1000100,1001000,1010000,1100000,
%U A038444 10000001,10000010,10000100,10001000,10010000,10100000,11000000,100000001,100000010,100000100
%N A038444 Sums of 2 distinct powers of 10.
%H A038444 Reinhard Zumkeller, <a href="/A038444/b038444.txt">Table of n, a(n) for n = 1..10000</a>
%F A038444 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
%p A038444 seq(seq(10^d + 10^j, j=0..d-1), d=1..10); # _Robert Israel_, Oct 14 2016
%t A038444 Sort[Total/@Subsets[10^Range[0,7],{2}]] (* _Harvey P. Dale_, Apr 20 2012 *)
%o A038444 (Haskell)
%o A038444 a038444 n = a038444_list !! (n-1)
%o A038444 a038444_list = 11 : f [11] 90 where
%o A038444    f xs@(x:_) z = ys ++ f ys (10 * z) where
%o A038444                   ys = (x + z) : map (* 10) xs
%o A038444 -- _Reinhard Zumkeller_, Jan 28 2015
%o A038444 (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
%o A038444 (Python)
%o A038444 from math import isqrt
%o A038444 def A038444(n): return 10**(m:=isqrt(n<<3)+1>>1)+10**(n-1-(m*(m-1)>>1)) # _Chai Wah Wu_, Mar 11 2025
%Y A038444 Subsequence of A052216 and of A007088.
%Y A038444 Cf. A018900.
%K A038444 nonn,easy
%O A038444 1,1
%A A038444 _Olivier Gérard_
%E A038444 Offset corrected by _Reinhard Zumkeller_, Jan 28 2015