A001510 a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1, with a(0) = 1, a(1) = 2.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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

Crossrefs

Cf. A001622, A002715.

Programs

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 *)

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

Extensions

Clarified definition, with thanks to Amiram Eldar, Feb 02 2022. - N. J. A. Sloane, Jan 09 2025