A228915 - OEIS

%I #27 Mar 18 2022 13:17:10

%S 10,11,12,13,14,15,16,17,18,100,20,21,22,23,24,25,26,27,28,101,30,31,

%T 32,33,34,35,36,37,38,102,40,41,42,43,44,45,46,47,48,103,50,51,52,53,

%U 54,55,56,57,58,104,60,61,62,63,64,65,66,67,68,105,70,71,72

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

%C This is a variant of A057168 for the base 10.

%C All integers except those in A051885 appear in this sequence.

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

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

%H Paul Tek, <a href="/A228915/b228915.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Tek, <a href="/A228915/a228915.txt">PARI program for this sequence</a>

%e To compute a(n):

%e (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),

%e (2) Increment D,

%e (3) Replace the digits after D by A051885((sum of the digits after D) - 1), left padded with zeros.

%e For n = 2930:

%e (1) We choose the 4th digit,

%e (2) We increment the 4th digit,

%e (3) We replace the last 3 digits with "029" (= A051885((9+3+0)-1) left padded with zeros to 3 digits).

%e Hence, a(2930) = 3029.

%t 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 *)

%o (PARI) See Link section.

%o (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

%o (Python)

%o def A228915(n):

%o     p = r = 0

%o     while True:

%o         d = n % 10

%o         if d < 9 and r: return (n+1)*10**p+A051885(r-1)

%o         n //= 10; r += d; p += 1

%o # (Based on Tek's PARI program.) - _M. F. Hasler_, Mar 15 2022

%Y Cf. A007953, A051885, A057168.

%K base,nonn

%O 1,1

%A _Paul Tek_, Sep 08 2013