|
|
A228915
|
|
Next larger integer with same digital sum (that is, sum of digits in base 10) as n.
|
|
9
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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)
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
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|