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Search: id:A132433
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| A132433 |
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a(1) = 2; for n>=2, a(n) = 8*a(n-1)+1. |
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+0
2
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| 2, 17, 137, 1097, 8777, 70217, 561737, 4493897, 35951177, 287609417, 2300875337, 18407002697, 147256021577, 1178048172617, 9424385380937, 75395083047497, 603160664379977, 4825285315039817, 38602282520318537, 308818260162548297, 2470546081300386377
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Quadratic radical circle dividers in multi-step manner, 17 being the famous Gauss discovery, 137 being my discovery. Also the core of the physical fine structure constant.
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REFERENCES
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Reeben,V.: The highly composite numbers by Srinivasa Ramanujan and the fundamental constants of physics. J. Madras Univ., Sect. B, 51 (Ramanujan's 100th birthday issue, with a Table of h.c.n.'s up to 10^102), (1988) 88-146.
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FORMULA
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G.f.: -x*(-2+x)/(-1+x)/(-1+8*x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=-1/7+(15/7)*8^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 08 2008
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CROSSREFS
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Cf. A132434.
Sequence in context: A077243 A037525 A037734 this_sequence A037557 A026941 A037493
Adjacent sequences: A132430 A132431 A132432 this_sequence A132434 A132435 A132436
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KEYWORD
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nonn
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AUTHOR
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Vello Reeben (reeben(AT)ut.ee), Aug 25 2007
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