A256112 Pandigitals in some base b (A061845) with an extra property: each number formed by the first i digits is divisible by i (digits in the pandigital base b) for 1 <= i <= b-1.

2, 19, 75, 99, 108, 135, 228, 2102, 8525, 10535, 13685, 13710, 26075, 31835, 44790, 203367, 247215, 477543, 518703, 576495, 620343, 743823, 3850399, 6996535, 6996871, 6996920, 7375543, 8947631, 11128712, 12306056, 78473956, 89789620, 156414388, 222029284, 306600196

Offset: 1

Author

Chai Wah Wu, Jun 07 2015

Keywords

• nonn
• base

Comments

A111456 is the subsequence of terms divisible by the considered base (which is the least b such b^b > a(n)).

Is it true that there are no terms for base b > 16 and b even?

Examples

			247215 = 2046513[7] (i.e., in base 7) is pandigital and 20[7] = 14 is even, 204[7] = 102 is divisible by 3, etc. up to 204651[7] = 35316 which is divisible by 6.
In contrast to A111456, the number as a whole does not need to be divisible by the considered base. - _M. F. Hasler_, May 27 2020
		

Links

• Hans Havermann and Giovanni Resta, Table of n, a(n) for n = 1..233 (first 163 terms from Chai Wah Wu)
• Hans Havermann, base-formatted (a=10, b=11, c=12, ..) terms, A111456 highlighted

Crossrefs

Cf. A111456.

Programs

Python

def dgen(n,b):
    if n == 1:
        t = list(range(b))
        for i in range(1,b):
            u = list(t)
            u.remove(i)
            yield i, u
    else:
        for d, v in dgen(n-1,b):
            for g in v:
                k = d*b+g
                if not k % n:
                    u = list(v)
                    u.remove(g)
                    yield k, u
A256112_list = lambda n: [a*k+b[0] for k in range(2, n) for a, b in dgen(k-1, k)]
print(A256112_list(10))

Extensions

Edited by M. F. Hasler, May 27 2020