A079497 a(1)=1; for n > 2, a(n) is the smallest integer > a(n-1) such that frac(sqrt(5)*a(n)) < frac(sqrt(5)*a(n-1)).
1, 5, 9, 13, 17, 89, 161, 233, 305, 1597, 2889, 4181, 5473, 28657, 51841, 75025, 98209, 514229, 930249, 1346269, 1762289, 9227465, 16692641, 24157817, 31622993, 165580141, 299537289, 433494437, 567451585, 2971215073, 5374978561
Offset: 1
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Crossrefs
Cf. A005246.
Programs
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Mathematica
nxt[{n_,a_,b_,c_,d_}]:={n+1,b,c,d,If[Mod[n,4]==1,6d-c,2d-c]}; NestList[nxt,{4,1,5,9,13},30][[All,2]] (* Harvey P. Dale, Mar 30 2022 *)
Formula
a(1)=1, a(2)=5, a(3)=9, a(4)=13; for n >= 4, if n == 1 (mod 4) then a(n+1) = 6 * a(n) - a(n-1); otherwise, a(n+1) = 2*a(n) - a(n-1).