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

0,2

Comments

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]

Links

Table of n, a(n) for n=0..36.

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

Example

For n=0, the least number with sum of digits 2*0+1=1 is 1, so a(0)=1.

Prog

(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

Crossrefs

Cf. A051885.

Sequence in context: A357677 A262029 A259380 * A119252 A283003 A329590

Adjacent sequences: A131665 A131666 A131667 * A131669 A131670 A131671

Keyword

nonn,base,changed

Author

Paul Curtz, Oct 03 2007

Status

approved