A052036 Smallest number that must be added to n to make or keep n palindromic.

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

Links

Table of n, a(n) for n=0..99.

Patrick De Geest, World!Of Numbers

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

Cf. A052037, A002113, A088997.

Sequence in context: A259567 A022966 A023452 * A304622 A178914 A143473

Adjacent sequences: A052033 A052034 A052035 * A052037 A052038 A052039

Keyword

nonn,base,easy

Author

Patrick De Geest, Dec 15 1999

Status

approved