A228915 Next larger integer with same digital sum (that is, sum of digits in base 10) as n.

10, 11, 12, 13, 14, 15, 16, 17, 18, 100, 20, 21, 22, 23, 24, 25, 26, 27, 28, 101, 30, 31, 32, 33, 34, 35, 36, 37, 38, 102, 40, 41, 42, 43, 44, 45, 46, 47, 48, 103, 50, 51, 52, 53, 54, 55, 56, 57, 58, 104, 60, 61, 62, 63, 64, 65, 66, 67, 68, 105, 70, 71, 72

Offset: 1

Author

Paul Tek, Sep 08 2013

Keywords

• base
• nonn

Comments

This is a variant of A057168 for the base 10.

All integers except those in A051885 appear in this sequence.

n+9 <= a(n) <= 10*n, for any n > 0.

a(n)-n is a multiple of 9, for any n > 0.

Examples

			To compute a(n):
(1) Choose the rightmost digit D of n strictly less than 9 and with at least one nonzero digit after it (note that D may be a leading zero),
(2) Increment D,
(3) Replace the digits after D by A051885((sum of the digits after D) - 1), left padded with zeros.
For n = 2930:
(1) We choose the 4th digit,
(2) We increment the 4th digit,
(3) We replace the last 3 digits with "029" (= A051885((9+3+0)-1) left padded with zeros to 3 digits).
Hence, a(2930) = 3029.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PARI program for this sequence

Crossrefs

Cf. A007953, A051885, A057168.

Programs

Mathematica

nli[n_]:=Module[{k=n+1,s=Total[IntegerDigits[n]]},While[Total[ IntegerDigits[ k]] !=s, k++]; k]; Array[nli,70] (* Harvey P. Dale, Sep 27 2016 *)

PARI

See Link section.

PARI

A228915(n,p=1,d,r)={while(8<(d=n%10) || !r, n\=10; r+=d; p*=10); n*p+p+A051885(r-1)} \\ (Based on the above program.) - M. F. Hasler, Mar 15 2022

Python

def A228915(n):
    p = r = 0
    while True:
        d = n % 10
        if d < 9 and r: return (n+1)*10**p+A051885(r-1)
        n //= 10; r += d; p += 1
# (Based on Tek's PARI program.) - M. F. Hasler, Mar 15 2022