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A346211
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Numbers m such that abs(K(m+1) - K(m)) = 1, where K(m) = A002034(m) is the Kempner function.
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2
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1, 2, 3, 4, 9, 15, 35, 63, 99, 175, 195, 483, 1443, 2057, 2115, 2299, 3363, 3843, 5082, 5475, 6723, 7865, 11235, 11913, 12005, 22747, 24963, 26978, 27555, 31683, 37635, 41514, 46255, 51075, 62464, 68643, 76704, 77283, 89375, 95874, 98595, 104975, 105412, 113398
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OFFSET
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1,2
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COMMENTS
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Florentin Smarandache (Muller, 1990) and Tutescu (1996) conjectured that there is no number m such that K(m) = K(m+1), and Weisstein (2004) verified it up to m = 10^9.
a(1)-a(40) were calculated by Earls (2005).
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REFERENCES
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Lucian Tutescu, On a Conjecture Concerning the Smarandache Function, Abstracts of Papers Presented to the Amer. Math. Soc., Vol. 17 (1996), p. 583.
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LINKS
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EXAMPLE
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1 is a term since K(2) - K(1) = 2 - 1 = 1.
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MATHEMATICA
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kempner[n_] := Module[{m = 1}, While[! Divisible[m!, n], m++]; m]; Position[Abs @ Differences @ Array[kempner, 500], 1] // Flatten
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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