A222810 Number of n-digit numbers N with distinct digits such that the reversal of N divides N.

9, 9, 3, 5, 3, 2, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane, Mar 10 2013

Keywords

• nonn
• base

Comments

Suggested by A214927.

a(n)=0 for all n > 6.

Examples

			Solutions with 1 through 6 digits:
[1, 2, 3, 4, 5, 6, 7, 8, 9],
[10, 20, 30, 40, 50, 60, 70, 80, 90],
[510, 540, 810],
[5610, 5940, 8712, 8910, 9801],
[65340, 87120, 87912],
[659340, 879120],
		

Crossrefs

Cf. A214927, A222809, A222811, A222812.

For the actual numbers see A223080.

Programs

Python

import collections
col = []
count = 0
for n in range(0, 9):
    a = 10**n
    stop = 10**(n+1)
    while a < stop:
        b = str(a)
        c = list(b)
        d = c[::-1]
        e = int("".join(c))
        f = int("".join(d))
        counter = collections.Counter(c)
        if e % f == 0 and counter.most_common(1)[0][1] == 1:
            count += 1
            col.append(a)
        a += 1
    print(n+1, " digits: ", count, " elements: ", col)
    count = 0
    col = []
# David Consiglio, Jr., Dec 04 2014

Extensions

a(8)-a(9) from David Consiglio, Jr., Dec 04 2014