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.

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

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: A246321 A104664 A338921 * A022856 A089071 A177205

Adjacent sequences: A333340 A333341 A333342 * A333344 A333345 A333346

Keyword

nonn

Author

Jinyuan Wang, Mar 31 2020

Status

approved