A070837 Smallest number k such that abs(k - R(k)) = 9n, where R(k) is digit reversal of k (A004086); or 0 if no such k exists.

10, 13, 14, 15, 16, 17, 18, 19, 90, 1011, 100, 0, 0, 0, 0, 0, 0, 0, 0, 1021, 1090, 103, 0, 0, 0, 0, 0, 0, 0, 1031, 1080, 0, 104, 0, 0, 0, 0, 0, 0, 1041, 1070, 0, 0, 105, 0, 0, 0, 0, 0, 1051, 1060, 0, 0, 0, 106, 0, 0, 0, 0, 1061, 1050, 0, 0, 0, 0, 107, 0, 0, 0, 1071, 1040, 0, 0, 0, 0, 0

Offset: 1

Author

Amarnath Murthy, May 12 2002

Keywords

• base
• nonn

Comments

If 9n < 1000, k has at most 5 digits, and abs(k - R(k)) = 9n, then 10 must divide n. - Sascha Kurz, Jan 02 2003

Crossrefs

Cf. A004086, A056965, A070838.

Programs

Mathematica

a = Table[0, {50}]; Do[d = Abs[n - FromDigits[ Reverse[ IntegerDigits[n]]]] / 9; If[d < 51 && a[[d]] == 0, a[[d]] = n], {n, 1, 10^7}]; a

Python

def back_difference(n):
    r = int(str(n)[::-1])
    return abs(r-n)
def a070837(n):
    i = 0
    while True:
        if back_difference(i)==9*n:
            return i
        i+=1
# Christian Perfect, Jul 23 2015

Extensions

More terms from Sascha Kurz, Jan 02 2003

a(21) corrected by Christian Perfect, Jul 23 2015