A199343 Least integer > n having a larger or the same digital sum as n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 11, 12, 13, 14, 15, 16, 17, 18, 19, 28, 21, 22, 23, 24, 25, 26, 27, 28, 29, 38, 31, 32, 33, 34, 35, 36, 37, 38, 39, 48, 41, 42, 43, 44, 45, 46, 47, 48, 49, 58, 51, 52, 53, 54, 55, 56, 57, 58, 59, 68, 61, 62, 63, 64, 65, 66, 67, 68, 69, 78, 71, 72, 73, 74, 75, 76, 77, 78, 79, 88, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98, 91, 92, 93, 94, 95, 96, 97, 98, 99, 189

Offset

0,2

Comments

If n does not end in 9, then a(n) = n + 1, else a(n) is obtained by increasing the last digit of n not equal to 9, and by decreasing the immediately following 9 by 1 (as to get an 8), which is equivalent to adding 9*10^(d-1) where d is the number of trailing 9's in n. In the first case the digital sum of a(n) is 1 more than that of n; in the second case these digital sums are equal.

Links

Table of n, a(n) for n=0..99.

Formula

a(n) = n + 1 unless n=9 (mod 10).

a(n) = n + 9*10^(valuation(n+1,10)-1) if this valuation (largest power of 10 to divide n+1) is positive.

The two cases can be unified as: a(n) = n + ceiling(9*10^(valuation(n+1,10)-1)).

Prog

(PARI) A199343(n)= n+if(n%10<9, 1, 9*10^(valuation(n+1, 10)-1))

Crossrefs

Cf. A199344.

Sequence in context: A335493 A319725 A048408 * A118765 A131646 A032864

Adjacent sequences: A199340 A199341 A199342 * A199344 A199345 A199346

Keyword

nonn,base

Author

M. F. Hasler, Nov 07 2011

Status

approved