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A333343 Least k such that f(k) < 0, where f(1) = n and f(k) = f(k-1)*2^(1/k) - 1 for k > 1. 0
2, 3, 5, 8, 12, 17, 22, 30, 38, 49, 60, 74, 90, 108, 129, 152, 177, 206, 238, 272, 310, 352, 397, 447, 500, 558, 620, 686, 758, 834, 916, 1003, 1096, 1194, 1298, 1409, 1526, 1649, 1779, 1916, 2060, 2212, 2371, 2538, 2713, 2896, 3087, 3287, 3496, 3714, 3941, 4178 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If f(k) = f(k-1)*c^(1/k) - 1 for k > 1 and c > e = 2.718281828..., then as long as f(1) is large enough, f(k) can always be positive.

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

For n=0, f(1) = 0 and f(2) = -1 < 0. Thus, a(0) = 2.

PROG

(PARI) a(n) = {my(k=1, f=n); while(f>0, f=f*sqrtn(2, k++)-1); k+!n; }

CROSSREFS

Cf. A333342.

Sequence in context: A028955 A246321 A104664 * A022856 A089071 A177205

Adjacent sequences:  A333340 A333341 A333342 * A333344 A333345 A333346

KEYWORD

nonn

AUTHOR

Jinyuan Wang, Mar 31 2020

STATUS

approved

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Last modified September 18 22:48 EDT 2020. Contains 337174 sequences. (Running on oeis4.)