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).

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.

Links

Table of n, a(n) for n=1..14.

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