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.
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, Vol. 54, No. 3 (1947), pp. 135-142.
FORMULA
a(n+2) = A002715(2*n) + 1. - R. J. Mathar, Apr 23 2007
a(n) = floor(1 + phi^(2^n)/2), where phi is the golden ratio (A001622) [Aho and Sloane, 1973]. - Amiram Eldar, Feb 02 2022
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
EXTENSIONS
Clarified definition, with thanks to Amiram Eldar, Feb 02 2022. - N. J. A. Sloane, Jan 09 2025
STATUS
approved