%I #30 Apr 28 2024 09:49:18
%S 1,3,5,7,9,29,49,69,89,199,399,599,799,999,2999,4999,6999,8999,19999,
%T 39999,59999,79999,99999,299999,499999,699999,899999,1999999,3999999,
%U 5999999,7999999,9999999,29999999,49999999,69999999,89999999,199999999
%N Smallest number whose sum of digits is 2n+1.
%C Numbers which can't be represented as the sum of two numbers with the same sum of digits in base 10 (according to _Daniel Starodubtsev_). More generally, this definition and the definition from the name of this sequence matches for any even base. - _Mikhail Kurkov_, May 19 2019 [verification needed]
%F a(n) = h(n,10)*10^g(n,10)-1, with f(n,k) = floor((n+1)/(k-1)) - floor(n/(k-1)), g(n,k) = floor(2*(n+1)/(k-1)) - f(n,k), h(n,k) = 2*(n+1) - (k-1)*g(n,k). - _Mikhail Kurkov_, May 19 2019
%e For n=0, the least number with sum of digits 2*0+1=1 is 1, so a(0)=1.
%o (PARI) a(n) = {my(k=0); while (sumdigits(k) != 2*n+1, k++); k;} \\ _Michel Marcus_, May 19 2019
%o (PARI) a(n) = if(n<5, return(2*n+1)); n-=5;[30, 50, 70, 90, 200, 400, 600, 800, 1000][n%9+1] * 100^(n\9)-1 \\ _David A. Corneth_, May 19 2019
%Y Cf. A051885.
%K nonn,base
%O 0,2
%A _Paul Curtz_, Oct 03 2007