OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link.
H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, Vol. 54, No. 3 (1947), pp. 135-142.
FORMULA
Apparently a(n+2) = A002715(2*n) + 1. - R. J. Mathar, Apr 23 2007
From Amiram Eldar, Feb 02 2022: (Start)
a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1.
a(n) = floor(1 + phi^(2^n)/2), where phi is the golden ratio (A001622) (Aho and Sloane, 1973). (End)
MATHEMATICA
(* a5 = A002715 *) a5[n_?OddQ] := a5[n] = 2*a5[n-1] + 1; a5[n_?EvenQ] := a5[n] = (a5[n-1]^2 - 3)/2; a5[0] = 3; a[n_] := a5[2*n - 4] + 1; a[0] = 1; a[1] = 2; Table[a[n], {n, 0, 8}] (* Jean-François Alcover, Jan 25 2013, after R. J. Mathar *)
Join[{1}, RecurrenceTable[{a[1] == 2, a[n] == 2*a[n - 1]*(a[n - 1] - 1)}, a, {n, 1, 8}]] (* Amiram Eldar, Feb 02 2022 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
STATUS
approved