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

1,1

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.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, PARI program for this sequence

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A007953, A051885, A057168.

Sequence in context: A115844 A008714 A058364 * A162790 A008713 A008712

Adjacent sequences: A228912 A228913 A228914 * A228916 A228917 A228918

Keyword

base,nonn

Author

Paul Tek, Sep 08 2013

Status

approved