VOOZH about

URL: https://oeis.org/A052036

⇱ A052036 - OEIS

login
A052036
Smallest number that must be added to n to make or keep n palindromic.
5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
OFFSET
0,13
FORMULA
a(n)=0 iff n is in A002113, otherwise a(n)=A052037(n)-1. - M. F. Hasler, Apr 26 2014
EXAMPLE
If n = 13 we need to add 9 to arrive at palindrome 22.
MATHEMATICA
snpal[n_]:=Module[{k=0, idn}, While[idn=IntegerDigits[n+k]; idn != Reverse[ idn], k++]; k]; Array[snpal, 100, 0] (* Harvey P. Dale, Nov 27 2012 *)
PROG
(PARI) a(n)=for(k=0, 9e19, is_A002113(n+k)&&return(k)) \\ For illustrative purpose only, inefficient for most large numbers. - M. F. Hasler, Apr 26 2014
(Python)
def A052036(n):
sl = len(str(n))
l, w = divmod(sl, 2)
l10 = 10**l
if w:
x = l+1
t = 10**(x-1)
t2 = t*10
for y in range(n//l10, t2):
k, m = y//10, 0
while k >= 10:
k, r = divmod(k, 10)
m = 10*m + r
z = y*t + 10*m + k
if z >= n:
return z-n
else:
x = l
t = 10**(x-1)
t2 = t*10
for y in range(n//l10, t2):
k, m = y, 0
while k >= 10:
k, r = divmod(k, 10)
m = 10*m + r
z = y*t2 + 10*m + k
if z >= n:
return z-n # Chai Wah Wu, Feb 05 2026
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Patrick De Geest, Dec 15 1999
STATUS
approved