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

%I A001510 M1301 N0499 #37 Jan 09 2025 08:18:26
%S A001510 1,2,4,24,1104,2435424,11862575248704,281441383062305809756861824,
%T A001510 158418504200047111075388369241884118003210485743490304
%N A001510 a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1, with a(0) = 1, a(1) = 2.
%D A001510 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001510 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001510 A. V. Aho and N. J. A. Sloane, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
%H A001510 A. V. Aho and N. J. A. Sloane, <a href="/A000058/a000058.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
%H A001510 H. E. Salzer, <a href="http://www.jstor.org/stable/2305906">The approximation of numbers as sums of reciprocals</a>, Amer. Math. Monthly, Vol. 54, No. 3 (1947), pp. 135-142.
%H A001510 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A001510 a(n+2) = A002715(2*n) + 1. - _R. J. Mathar_, Apr 23 2007
%F A001510 a(n) = floor(1 + phi^(2^n)/2), where phi is the golden ratio (A001622) [Aho and Sloane, 1973]. -  _Amiram Eldar_, Feb 02 2022
%t A001510 (* 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_ *)
%t A001510 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 *)
%Y A001510 Cf. A001622, A002715.
%K A001510 nonn,nice
%O A001510 0,2
%A A001510 _N. J. A. Sloane_
%E A001510 Clarified definition, with thanks to _Amiram Eldar_, Feb 02 2022. - _N. J. A. Sloane_, Jan 09 2025