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A123901
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(n+3)/GCD(d(n),d(n+2)) where d(n) = cancellation factor in reducing Sum_{k=0...n} 1/k! to lowest terms.
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7
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3, 4, 5, 3, 7, 4, 9, 1, 11, 6, 13, 7, 3, 8, 17, 9, 19, 2, 21, 11, 23, 12, 5, 1, 27, 14, 29, 3, 31, 16, 33, 17, 7, 18, 37, 19, 3, 4, 41, 21, 43, 22, 9, 23, 47, 24, 49, 5, 51, 2, 53, 27, 11, 28, 57, 29, 59, 6, 61, 31, 63, 32, 1, 33, 67, 34, 69, 7, 71, 36, 73, 1, 15, 38, 77, 3, 79, 8, 81
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
| J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
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FORMULA
| a(n) = (n+3)/GCD(A093101(n),A093101(n+2)) where A093101(n) = GCD(n!,1+n+n(n-1)+...+n!)
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EXAMPLE
| a(5) = 4 because (5+3)/GCD(d(5),d(7)) = 8/GCD(2,20) = 8/2 = 4.
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MATHEMATICA
| (A[n_] := If[n==0, 1, n*A[n-1]+1]; d[n_] := GCD[A[n], n! ]; Table[(n+3)/GCD[d[n], d[n+2]], {n, 0, 79}])
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CROSSREFS
| Cf. A000522, A061354, A093101, A123899, A123900.
Sequence in context: A137926 A090395 A168485 * A093395 A176774 A126352
Adjacent sequences: A123898 A123899 A123900 * A123902 A123903 A123904
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 18 2006
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