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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
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.
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
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