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A116440
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Numbers k which when sandwiched between two 5's give a multiple of k.
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9
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1, 5, 11, 13, 35, 55, 65, 77, 91, 137, 365, 685, 9091, 49505, 909091, 5882353, 10989011, 12987013, 20242915, 23923445, 34965035, 37593985, 52631579, 54945055, 64935065, 76923077, 90909091, 495049505, 1976284585, 4132231405, 4347826087, 9090909091, 13698630137
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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137 belongs since 51375 is a multiple 137 (137*375).
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MAPLE
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a:=proc(n) local nn: nn:=convert(n, base, 10): if type((5+10*n+5*10^(nops(nn)+1))/n, integer)=true then n else fi end: seq(a(n), n=1..10000); # Emeric Deutsch, Feb 28 2006
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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[5, 10] (* Ray Chandler, May 11 2007 *)
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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, 5]
for k in count(2):
t = 5*(10**(k+1) + 1)
yield from (t//i for i in range(500, 50, -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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