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

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,18,0,0,0,-1).

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).

From Chai Wah Wu, Jun 16 2026: (Start)

a(n) = 18*a(n-4) - a(n-8) for n > 8.

G.f.: x*(-x^7 - x^6 - x^5 - x^4 + 13*x^3 + 9*x^2 + 5*x + 1)/(x^8 - 18*x^4 + 1). (End)

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 *)

Crossrefs

Cf. A005246.

Sequence in context: A125018 A074787 A255645 * A314701 A314702 A314703

Adjacent sequences: A079494 A079495 A079496 * A079498 A079499 A079500

Keyword

nonn

Author

Benoit Cloitre, Jan 20 2003

Status

approved