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A116163
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Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 1.
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8
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1, 5, 61, 65479, 84289, 106609, 225649, 275599, 453589, 1869505, 2272555, 2738291, 3221951, 1667833021, 2475062749, 2525062249, 3500010739, 9032526511, 9225507211, 1753016898055, 1860598847399, 3233666953849, 3379207972471, 5632076031055, 5823639407489
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OFFSET
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1,2
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COMMENTS
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Also numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 3.
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LINKS
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EXAMPLE
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1 is a member since 12 = 3*4; also 10 = 2*5.
5 is a member since 56 = 7*8; also 54 = 6*9.
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MATHEMATICA
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Union @@ ((y /. List@ ToRules@ Reduce[x (x+1) == 10^# y +y+1 && x>0 && 10^(#-1) <= y+1 < 10^#, {x, y}, Integers]) & /@ Range[13] /. y->{}) (* Giovanni Resta, Jul 08 2018 *)
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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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