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 A179332 a(1)=1; for each n > 1, a(n) is the smallest number such that Sum_{i=1..n} 1/a(i)^2 < sqrt(2). 2
 1, 2, 3, 5, 9, 37, 195, 8584, 1281621, 1325419784, 40182098746967, 203448501599750774078, 4275655952199444141114482835180, 10920781877316031992615629928696178128586477545 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In other words, the sequence is the lexicographically first infinite sequence of positive integers whose squared reciprocals sum to less than sqrt(2). After a(1)=1, each term is the smallest number that will not cause the sum of the squares of the reciprocals to exceed the square root of 2. LINKS FORMULA a(n+1) = ceiling(1/sqrt(sqrt(2) - Sum_{i=1..n} 1/a(i)^2)). - R. J. Mathar, Jul 11 2010 EXAMPLE a(1)=1; 1/1^2 = 1; a(2)=2; 1 + 1/2^2 = 5/4 = 1.25; a(3)=3; 5/4 + 1/3^2 = 49/36 = 1.3611111111...; a(4)=5; 49/36 + 1/5^2 = 1261/900 = 1.4011111111...; a(5)=9; 1261/900 + 1/9^2 = 11449/8100 = 1.4134567901...; (sums approach sqrt(2) = 1.4142135623...). MAPLE Digits := 200 : A179332 := proc(n) option remember; if n = 1 then 1; else sqrt(2)-add( 1/procname(i)^2, i=1..n-1) ; ceil( 1/sqrt(%)) ; end if; end proc: seq(A179332(n), n=1..14) ; # R. J. Mathar, Jul 11 2010 CROSSREFS Cf. A216245. Sequence in context: A118998 A276410 A003432 * A081938 A129500 A250745 Adjacent sequences:  A179329 A179330 A179331 * A179333 A179334 A179335 KEYWORD easy,nonn AUTHOR Ben Paul Thurston, Jul 10 2010 EXTENSIONS More terms from R. J. Mathar, Jul 11 2010 Name changed, comments expanded, and example corrected and expanded by Jon E. Schoenfield, Feb 28 2014 STATUS approved

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Last modified January 16 17:49 EST 2022. Contains 350376 sequences. (Running on oeis4.)