A001510 From a slowly converging series. (Formerly M1301 N0499)

1, 2, 4, 24, 1104, 2435424, 11862575248704, 281441383062305809756861824, 158418504200047111075388369241884118003210485743490304

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

Table of n, a(n) for n=0..8.

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.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

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

Cf. A001622, A002715.

Sequence in context: A341633 A128299 A143672 * A103099 A342665 A266495

Adjacent sequences: A001507 A001508 A001509 * A001511 A001512 A001513

Keyword

nonn,nice

Author

N. J. A. Sloane

Status

approved