A131668 Smallest number whose sum of digits is 2n+1.
1, 3, 5, 7, 9, 29, 49, 69, 89, 199, 399, 599, 799, 999, 2999, 4999, 6999, 8999, 19999, 39999, 59999, 79999, 99999, 299999, 499999, 699999, 899999, 1999999, 3999999, 5999999, 7999999, 9999999, 29999999, 49999999, 69999999, 89999999, 199999999
Offset: 0
Examples
For n=0, the least number with sum of digits 2*0+1=1 is 1, so a(0)=1.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,100,-100).
Programs
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PARI
a(n) = {my(k=0); while (sumdigits(k) != 2*n+1, k++); k;} \\ Michel Marcus, May 19 2019 -
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
Formula
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
Comments