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A116443
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Numbers k which when sandwiched between two 8's give a multiple of k.
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9
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1, 2, 4, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88, 91, 137, 146, 274, 292, 548, 584, 9091, 19802, 39604, 79208, 909091, 5882353, 10989011, 12987013, 13986014, 15037594, 16194332, 19138756, 21978022, 25974026, 27972028, 30075188, 32388664, 38277512, 43956044
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OFFSET
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1,2
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LINKS
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EXAMPLE
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91 belongs since 8918 is a multiple of 91 (91*98 = 8918).
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MATHEMATICA
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f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[8, 8] f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[9, 8] (* Ray Chandler, May 11 2007 *)
Select[Range[301*10^5], Divisible[FromDigits[Join[{8}, IntegerDigits[#], {8}]], #]&] (* Harvey P. Dale, Aug 27 2019 *)
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PROG
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(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
yield from [1, 2, 4, 8]
for k in count(2):
t = 8*(10**(k+1) + 1)
yield from (t//i for i in range(800, 80, -1) if t%i == 0)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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