Search: id:A001146
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%I A001146 M1297 N0497
%S A001146 2,4,16,256,65536,4294967296,18446744073709551616,
%T A001146 340282366920938463463374607431768211456,
%U A001146 115792089237316195423570985008687907853269984665640564039457584007913129639936
%N A001146 2^(2^n).
%C A001146 Or, write previous term in base 2, read in base 4.
%C A001146 a(1) = 2, a(n) = smallest power of 2 which does not divide the product 
               of all previous terms.
%C A001146 Number of truth tables generated by boolean expressions of n variables. 
               - C. Bradford Barber (bradb(AT)shore.net), Dec 27 2005
%C A001146 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.
%C A001146 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)
%D A001146 J. H. Conway, Sphere packings, lattices, codes and greed, pp. 45-55 of 
               Proc. Intern. Congr. Math., Vol. 2, 1994.
%D A001146 R. Ondrejka, Exact values of 2^n, n=1(1)4000, Math. Comp., 23 (1969), 
               456.
%D A001146 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001146 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001146 A. V. Aho and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               doc/doubly.html">Some doubly exponential sequences</a>, Fib. Quart., 
               11 (1973), 429-437.
%H A001146 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IrrationalitySequence.html">Link to a section of The World of Mathematics.</
               a>
%H A001146 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               QuadraticRecurrenceEquation.html">Quadratic Recurrence Equation</
               a>
%H A001146 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CoinTossing.html">Coin Tossing</a>
%H A001146 <a href="Sindx_Aa.html#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 
               + ...</a>
%F A001146 a(n+1) = (a(n))^2
%F A001146 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
%F A001146 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
%t A001146 lst={};Do[AppendTo[lst,2^(2^n)],{n,12}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Mar 01 2009]
%Y A001146 Cf. A026477, A062090, A062091, A000215, A112535, A155538.
%Y A001146 Sequence in context: A109457 A105788 A071008 this_sequence A114641 A152690 
               A001128
%Y A001146 Adjacent sequences: A001143 A001144 A001145 this_sequence A001147 A001148 
               A001149
%K A001146 nonn,easy,nice
%O A001146 0,1
%A A001146 N. J. A. Sloane (njas(AT)research.att.com).

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