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A059186
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Engel expansion of Pi^2/6, or zeta(2) = 1.64493.
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3
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1, 2, 4, 7, 9, 22, 35, 79, 2992, 3597, 17523, 28632, 41470, 53093, 57406, 14504930, 42622213, 188335162, 322429556, 1023003875, 1328535963, 3138645732, 11618168524, 137721814936, 156929353744, 166732460513, 813398686532
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OFFSET
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1,2
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COMMENTS
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Cf. A006784 for definition of Engel expansion.
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REFERENCES
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F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
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LINKS
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F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
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MATHEMATICA
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EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
EngelExp[N[Pi^2/6, 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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