A175539 a(1)=1, then a(n) = smallest number whose square is larger than 2*(a(n-1))^2.

1, 2, 3, 5, 8, 12, 17, 25, 36, 51, 73, 104, 148, 210, 297, 421, 596, 843, 1193, 1688, 2388, 3378, 4778, 6758, 9558, 13518, 19118, 27037, 38237, 54076, 76476, 108154, 152953, 216309, 305908, 432620, 611818, 865242, 1223637, 1730485, 2447276, 3460971

Offset

1,2

Comments

The sequence satisfies an almost recurrence relation, that is, there are 4 sequences b_0, b_1, b_2, b_3 taking values in {-2,-1,1,2} such that 2b_0(n)a(n) + 2b_1(n)a(n+1) + b_2(n)a(n+2) + b_3(n)a(n+3) = 0. For instance, we have a(103) - a(102) - 2a(101) + 2a(100) = 0, 2a(106) - a(105) - 4a(104) + 2a(103) = 0. - Benoit Cloitre, Oct 16 2012

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = ceiling(sqrt(2)*a(n-1)) with a(1)=1. - Benoit Cloitre, Oct 16 2012

Mathematica

NestList[Floor[Sqrt[2#^2]]+1&, 1, 50] (* Harvey P. Dale, Oct 19 2014 *)

Prog

(PARI) a=1; s=[a]; for(i=2, 100, a=1+sqrtint(2*a^2); s=concat(s, a)); s
(PARI) a(n)=if(n<2, 1, floor(sqrt(2)*a(n-1))) \\ Benoit Cloitre, Oct 16 2012

Crossrefs

Cf. A087057 (smallest number whose square is larger than 2*n^2).

Sequence in context: A318028 A373296 A200661 * A260795 A111388 A127884

Adjacent sequences: A175536 A175537 A175538 * A175540 A175541 A175542

Keyword

nonn

Author

Zak Seidov, Jun 14 2010

Status

approved