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A068601
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a(n) = n^3 - 1.
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37
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0, 7, 26, 63, 124, 215, 342, 511, 728, 999, 1330, 1727, 2196, 2743, 3374, 4095, 4912, 5831, 6858, 7999, 9260, 10647, 12166, 13823, 15624, 17575, 19682, 21951, 24388, 26999, 29790, 32767, 35936, 39303, 42874, 46655, 50652, 54871, 59318, 63999, 68920
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OFFSET
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1,2
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COMMENTS
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a(n) is the least positive integer k such that k can only contain 'n-1' in exactly 2 different bases B, where 1 < B <= k.
Numbers k such that for every nonnegative integer m, k^(3*m+1) + k^(3*m) is a cube. - Arkadiusz Wesolowski, Aug 10 2013
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LINKS
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FORMULA
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4*a(m^2-2*m+2) = (m^2-m+1)^3 + (m^2-m-1)^3 + (m^2-3*m+3)^3 + (m^2-3*m+1)^3. - Bruno Berselli, Jun 23 2014
Product_{n>=2} (1 + 1/a(n)) = 3*Pi*sech(sqrt(3)*Pi/2). - Amiram Eldar, Jan 20 2021
E.g.f.: 1 + exp(x)*(x^3 + 3*x^2 + x - 1). - Stefano Spezia, Jul 06 2021
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EXAMPLE
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For n=6; 215 written in bases 6 and 42 is 555, 55 and (555, 55) are exactly 2 different bases.
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MAPLE
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {0, 7, 26, 63}, 50]] (* Vincenzo Librandi, Mar 11 2012 *)
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PROG
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(PARI) a(n)=n^3-1
(Python) for n in range(1, 50): print(n**3-1, end=', ') # Stefano Spezia, Nov 21 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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