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A211667 Number of iterations sqrt(sqrt(sqrt(...(n)...))) such that the result is < 2. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Different from A001069, but equal for n < 256.

LINKS

Table of n, a(n) for n=1..86.

FORMULA

a(2^(2^n)) = a(2^(2^(n-1)))+1, for n>=1.

G.f.: g(x)= 1/(1-x)*sum_{k=0..infinity} x^(2^(2^k)). The explicit first terms of the g.f. are

g(x)=(x^2+x^4+x^16+x^256+x^65536+…)/(1-x).

EXAMPLE

a(n)=1, 2, 3, 4, 5 for n=2^1, 2^2, 2^4, 2^8, 2^16 =2, 4, 16, 256, 65536.

CROSSREFS

Cf. A001069, A010096, A211662, A211668, A211670.

Sequence in context: A151659 A057467 A074594 * A001069 A156877 A110591

Adjacent sequences:  A211664 A211665 A211666 * A211668 A211669 A211670

KEYWORD

base,nonn

AUTHOR

Hieronymus Fischer, Apr 30 2012

STATUS

approved

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Last modified August 18 18:24 EDT 2018. Contains 313834 sequences. (Running on oeis4.)