OFFSET
0,1
COMMENTS
Eventually periodic with period 4.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).
FORMULA
a(n) = 1+(1+(-1)^n)*(9+4*i^n)/2 - 7*A000007(n), where i is the imaginary unit. - Bruno Berselli, Mar 08 2011 - Mar 15 2011
From Amiram Eldar, Nov 13 2023: (Start)
Multiplicative with a(2) = 6, a(2^e) = 14 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 5/2^s + 1/2^(2*s-3)). (End)
EXAMPLE
7.87400787401181101968503444... = 7 + 1/(1 + 1/(6 + 1/(1 + 1/(14 + ...)))). - Harry J. Smith, Jun 07 2009
MATHEMATICA
ContinuedFraction[Sqrt[62], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
Join[{7}, LinearRecurrence[{0, 0, 0, 1}, {1, 6, 1, 14}, 72]] (* Ray Chandler, Aug 25 2015 *)
PadRight[{7}, 120, {14, 1, 6, 1}] (* Harvey P. Dale, Jan 20 2019 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 22000); x=contfrac(sqrt(62)); for (n=0, 20000, write("b010146.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009
(Magma) [7] cat &cat[ [1, 6, 1, 14]: n in [1..18]]; // Bruno Berselli, Mar 08 2011
CROSSREFS
KEYWORD
nonn,cofr,easy,mult
AUTHOR
STATUS
approved