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A138761
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a(n) is the smallest member of A000522 divisible by 2^n, where A000522(m) = total number of arrangements of a set with m elements.
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3
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OFFSET
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0,2
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COMMENTS
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a(n) < A000522(2^n) for n > 0; see Sondow and Schalm, Proposition A.13 part (ii).
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REFERENCES
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J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.
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LINKS
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FORMULA
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EXAMPLE
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a(5) = A000522(19) = 330665665962404000 because that is the smallest member of A000522 divisible by 2^5.
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MATHEMATICA
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a522[n_] := E Gamma[n + 1, 1];
b[1] = 1; b[n_] := b[n] = For[k = b[n - 1], True, k++, If[Mod[a522[k], 2^n] == 0, Return[k]]];
a[0] = 1; a[n_] := a522[b[n]];
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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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