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 A001069 Log2*(n) (version 2): take log_2 of n this many times to get a number < 2. 16
 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS From Hieronymus Fischer, Apr 08 2012: (Start) In terms of A010096 the definition could read: "Number of iterations log_2(log_2(log_2(...(n)...))) such that the result is < 2". With the only difference in the termination criterion, the definition is essentially the same as A010096. If we change the definition to " ...number < 1" we get A010096. Therefore we get A010096 when adding 1 to each term. (End) LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA From Hieronymus Fischer, Apr 08 2012: (Start) a(n) = A010096(n)-1. With the exponentiation definition E_{i=1..n} c(i) := c(1)^(c(2)^(c(3)^(...(c(n-1)^(c(n))))...))); E_{i=1..0} := 1; example: E_{i=1..4} 2 = 2^(2^(2^2)) = 2^16, we get: a(E_{i=1..n} 2) = a(E_{i=1..n-1} 2) +1, for n>=1. G.f.: g(x) = 1/(1-x)*Sum_{k >= 1} x^(E_{i=1..k} 2). The explicit first terms of this g.f. are g(x) = (x^2+x^4+x^16+x^65536+...)/(1-x). (End) EXAMPLE a(n)=1, 2, 3, 4, 5, ... for n=2, 2^2, 2^2^2, 2^2^2^2, 2^2^2^2^2, ... =2, 4, 16, 65536, 2^65536, ... MATHEMATICA f[n_] := Length@ NestWhileList[ Log[2, #] &, n, # >= 2 &] - 1; Array[f, 105] (* Robert G. Wilson v, Apr 19 2012 *) CROSSREFS Cf. A010096 (version 1), A230864 (version 3). Sequence in context: A057467 A074594 A211667 * A156877 A110591 A105209 Adjacent sequences: A001066 A001067 A001068 * A001070 A001071 A001072 KEYWORD nonn,easy AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)