0,1

Or, write previous term in base 2, read in base 4.

a(1) = 2, a(n) = smallest power of 2 which does not divide the product of all previous terms.

Number of truth tables generated by boolean expressions of n variables. - C. Bradford Barber (bradb(AT)shore.net), Dec 27 2005

Comments from Ross Drewe (rd(AT)labyrinth.net.au), Feb 13 2008: (Start) Or, number of distinct n-ary operators in a binary logic. The total number of n-ary operators in a k-valued logic is T = k^(k^n), i.e. if S is a set of k elements, there are T ways of mapping an ordered subset of n elements from S to an element of S. Some operators are "degenerate": the operator has arity p, if only p of the n input values influence the output. Therefore the set of operators can be partitioned into n+1 disjoint subsets representing arities from 0 to n.

n = 2, k = 2 gives the familiar Boolean operators or functions, C = F(A,B). There are 2^2^2 = 16 operators, composed of: arity 0: 2 operators (C = 0 or 1), arity 1: 4 operators (C = A, B, not(A), not(B)), arity 2: 10 operators (including well-known pairs AND/NAND, OR/NOR, XOR/EQ). (End)

J. H. Conway, Sphere packings, lattices, codes and greed, pp. 45-55 of Proc. Intern. Congr. Math., Vol. 2, 1994.

R. Ondrejka, Exact values of 2^n, n=1(1)4000, Math. Comp., 23 (1969), 456.

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).

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Quadratic Recurrence Equation

Eric Weisstein's World of Mathematics, Coin Tossing

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

a(n+1) = (a(n))^2

1 = Sum(0 through infinity) a(n)/A051179(n+1) = 2/3 + 4/15 + 16/255 + 256/65535...; with partial sums: 2/3, 14/15, 254/255, 65534/65535... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2003

Generating function: f(x)=1/(1-2x). Note: the generating function is not for a(n) but for for log_2(a(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 19 2006

lst={}; Do[AppendTo[lst, 2^(2^n)], {n, 12}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2009]

Cf. A026477, A062090, A062091, A000215, A112535, A155538.

Sequence in context: A109457 A105788 A071008 this_sequence A114641 A152690 A001128

Adjacent sequences: A001143 A001144 A001145 this_sequence A001147 A001148 A001149

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).