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Search: id:A059185
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| A059185 |
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Engel expansion of Pi^2 = 9.8696. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 9, 28, 45, 72, 111, 329, 415, 846, 1488, 5684, 1895742, 2890879, 5388452, 18083303, 30915293, 32699271, 38719784, 70637726, 118179186, 151342409, 995604288, 1839673662, 5342025157
(list; graph; listen)
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OFFSET
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1,10
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COMMENT
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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.
P. Erdos and J. O. Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..300
Index entries for sequences related to Engel expansions
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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 ]}&, {Ceiling[ 1/(A-Floor[ A ]) ], A-Floor[ A ]}, n-1 ] ]
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CROSSREFS
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Adjacent sequences: A059182 A059183 A059184 this_sequence A059186 A059187 A059188
Sequence in context: A127207 A089047 A036811 this_sequence A133948 A078935 A129768
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)
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