This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A134473 a(n) = the smallest positive integer such that sum{k=1 to n} 1/a(k) is <= product{j=1 to n} 1/(1 +1/a(j)), for every positive integer n. 5
 2, 10, 265, 186534, 39698716206, 9708281043219621795399, 485147416562376967927656482516055847985046599, 261312356099926248292437979417147998592741394591619008401746229884484893481820640113595606 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS sum{k=1 to n} 1/a(k) increases, but is bounded from above (by the product). While product{j=1 to n} 1/(1 +1/a(j)) decreases and is bounded from below (by the sum). The sum and the product then approach the same constant, which is approximately .6037789..., if their difference approaches 0. Does this constant have a closed form in terms of known constants, if the constant exists? LINKS FORMULA For n >= 2, if x = product{j=1 to n-1} 1/(1 +1/a(j)) and y = sum{k=1 to n-1} 1/a(k), then a(n) = ceiling[(1 + y + sqrt((y-1)^2 + 4x))/(2(x-y))]. EXAMPLE sum{k=1 to 2} 1/a(k) = 3/5 and product{j=1 to 2} 1/(1 +1/a(j)) = 20/33. For m = any positive integer <= 264, 3/5 + 1/m is > 20/33/(1 + 1/m). But if m = 265, then 3/5 + 1/m = 32/53 is <= 20/33/(1 + 1/m) = 2650/4389. So a(3) = 265. MAPLE Digits := 220 ; A134473 := proc(n) option remember ; local su, mu ; if n =1 then 2; else su := add(1/procname(k), k=1..n-1) ; mu := mul(1/(1+1/procname(j)), j=1..n-1) ; ceil( (1+su+sqrt((su-1)^2+4*mu))/2/(mu-su) ) ; fi; end: seq(A134473(n), n=1..9) ; [From R. J. Mathar, Jul 20 2009] CROSSREFS Cf. A134474, A134475, A134476, A134477. Sequence in context: A193482 A225371 A088310 * A005154 A074056 A206158 Adjacent sequences:  A134470 A134471 A134472 * A134474 A134475 A134476 KEYWORD nonn AUTHOR Leroy Quet Oct 27 2007 EXTENSIONS More terms from R. J. Mathar, Jul 20 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .