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Search: id:A001146
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| A001146 |
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2^(2^n).
(Formerly M1297 N0497)
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+0
25
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| 2, 4, 16, 256, 65536, 4294967296, 18446744073709551616, 340282366920938463463374607431768211456
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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)
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REFERENCES
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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.
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LINKS
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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 + ...
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FORMULA
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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
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CROSSREFS
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Cf. A026477, A062090, A062091, A000215, A112535.
Adjacent sequences: A001143 A001144 A001145 this_sequence A001147 A001148 A001149
Sequence in context: A109457 A105788 A071008 this_sequence A114641 A001128 A124436
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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