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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.

%I A256112 #31 Jun 06 2020 16:34:38
%S A256112 2,19,75,99,108,135,228,2102,8525,10535,13685,13710,26075,31835,44790,
%T A256112 203367,247215,477543,518703,576495,620343,743823,3850399,6996535,
%U A256112 6996871,6996920,7375543,8947631,11128712,12306056,78473956,89789620,156414388,222029284,306600196
%N 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.
%C A256112 A111456 is the subsequence of terms divisible by the considered base (which is the least b such b^b > a(n)).
%C A256112 Is it true that there are no terms for base b > 16 and b even?
%H A256112 Hans Havermann and Giovanni Resta, <a href="/A256112/b256112.txt">Table of n, a(n) for n = 1..233</a> (first 163 terms from Chai Wah Wu)
%H A256112 Hans Havermann, <a href="http://chesswanks.com/num/a256112.pdf">base-formatted (a=10, b=11, c=12, ..) terms, A111456 highlighted</a>
%e A256112 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.
%e A256112 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
%o A256112 (Python)
%o A256112 def dgen(n,b):
%o A256112     if n == 1:
%o A256112         t = list(range(b))
%o A256112         for i in range(1,b):
%o A256112             u = list(t)
%o A256112             u.remove(i)
%o A256112             yield i, u
%o A256112     else:
%o A256112         for d, v in dgen(n-1,b):
%o A256112             for g in v:
%o A256112                 k = d*b+g
%o A256112                 if not k % n:
%o A256112                     u = list(v)
%o A256112                     u.remove(g)
%o A256112                     yield k, u
%o A256112 A256112_list = lambda n: [a*k+b[0] for k in range(2, n) for a, b in dgen(k-1, k)]
%o A256112 print(A256112_list(10))
%Y A256112 Cf. A111456.
%K A256112 nonn,base
%O A256112 1,1
%A A256112 _Chai Wah Wu_, Jun 07 2015
%E A256112 Edited by _M. F. Hasler_, May 27 2020