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A256112
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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
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PROG
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(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)]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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