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A291215
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Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 7.
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6
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1014492753623188405797, 1159420289855072463768, 1304347826086956521739, 10144927536231884057971014492753623188405797, 11594202898550724637681159420289855072463768, 13043478260869565217391304347826086956521739, 101449275362318840579710144927536231884057971014492753623188405797
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OFFSET
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1,1
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COMMENTS
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x = (10^21 - 7)/69 = 14492753623188405797.
a(1) = 7*x*10 + 7, a(2) = 8*x*10 + 8, a(3) = 9*x*10 + 9.
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LINKS
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FORMULA
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a(3k-2) = 7(10^(22k)-1)/69.
a(3k-1) = 8(10^(22k)-1)/69.
a(3k) = 9(10^(22k)-1)/69.
a(n+6) = (10^22+1) a(n+3) - 10^22 a(n).
G.f.: (1304347826086956521739*x^2 + 1159420289855072463768*x + 1014492753623188405797)/
(10^22*x^6 - (10^22+1)*x^3 + 1). (End)
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EXAMPLE
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b = 101449275362318840579.
a(1) = b*10 + 7,
7*a(1) = 7101449275362318840579 = 7*10^21 + b.
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MAPLE
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seq(seq(y*((10^(22*k)-1)/69), y=7..9), k=1..6); # Robert Israel, Aug 22 2017
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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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STATUS
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approved
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