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A283754
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The smallest number k such that k*2^n mod 3^n = 1.
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1
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2, 7, 17, 76, 38, 262, 1589, 4075, 11879, 35464, 17732, 363160, 181580, 90790, 9611333, 11980120, 92083502, 175181914, 862431935, 2174608168, 1087304084, 543652042, 271826021, 235493860078, 117746930039, 1329806379184, 664903189592, 332451594796, 166225797398, 68713490263582, 446139009321089
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OFFSET
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1,1
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COMMENTS
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a(n) is the coefficient "a" in the Diophantine equation with two coefficients a and b, a * 2^n - b * 3^n = 1.
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LINKS
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FORMULA
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a(n) = ((3^n + 1)/2)^n mod 3^n (proved).
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EXAMPLE
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2 * 2^1 mod 3^1 = 1, 7 * 2^2 mod 3^2 =1, 17 * 2^3 mod 3^3 = 1...
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MAPLE
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MATHEMATICA
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PROG
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(PARI) a(n)= my(z=3^n); lift( Mod((z + 1)/2, z)^n); \\ Joerg Arndt, Mar 24 2017
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CROSSREFS
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KEYWORD
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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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