A115927 a(n) is the number of k such that k and n*k, taken together, are pandigital.

0, 48, 6, 8, 12, 0, 1, 16, 3, 0, 0, 1, 1, 6, 3, 1, 19, 6, 4, 12, 0, 3, 3, 4, 3, 9, 2, 1, 8, 2, 0, 16, 1, 3, 14, 0, 3, 7, 3, 4, 0, 3, 1, 13, 4, 1, 6, 0, 1, 12, 0, 2, 28, 1, 4, 6, 1, 3, 6, 3, 0, 28, 1, 1, 10, 1, 1, 4, 5, 7, 0, 3, 3, 11, 0, 2, 8, 1, 1, 46, 0, 0, 5, 3, 1, 7, 5, 6, 8, 3, 0, 13, 2, 3

Offset

1,2

Comments

There are 1549586 nonzero terms in a(n). The largest n for which a(n) > 0 is 987654320. The largest a(n) is a(2) = 48. - Chai Wah Wu, May 24 2015

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

a(7)=1 since there is only one number, k=14076, such that k and 7*k=98532.
a(9)=3 since there are 3 such numbers: 10638, 10647 and 10836.

Prog

(Python)
from itertools import permutations
l = {}
for d in permutations('0123456789', 10):
    if d[0] != '0':
        for i in range(9):
            if d[i+1] != '0':
                q, r = divmod(int(''.join(d[:i+1])), int(''.join(d[i+1:])))
                if not r:
                    if q in l:
                        l[q] += 1
                    else:
                        l[q] = 1
A115927_list = [0]*max(l)
for d in l:
    A115927_list[d-1] = l[d] # Chai Wah Wu, May 24 2015

Crossrefs

Cf. A054383, A115922, A115923, A115924, A115925, A114126.

Essentially the same as A069012.

Sequence in context: A037941 A229190 A069012 * A298619 A298831 A087407

Adjacent sequences: A115924 A115925 A115926 * A115928 A115929 A115930

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Status

approved