A343802 Least positive integer k such that Sum_{i=1..k} phi(i) >= 10^n.

1, 5, 18, 57, 181, 573, 1814, 5736, 18138, 57357, 181380, 573574, 1813799, 5735737, 18137993, 57357372, 181379937, 573573721, 1813799364, 5735737209, 18137993642, 57357372095, 181379936423, 573573720955, 1813799364234, 5735737209545, 18137993642342, 57357372095455

Offset

0,2

Comments

Least integer k such that A002088(k) >= 10^n.

Since A002088(k) = (3*k^2)/(Pi^2) + O(k log k), the digits of a(n) for n even (resp. odd) approach the decimal digits of Pi/sqrt(3)=1.8137993642342... and Pi*sqrt(10/3)=5.7357372095454... resp.

Conjecture: For n even, either a(n) = floor(Pi/sqrt(3)*10^(n/2)) or a(n) = floor(Pi/sqrt(3)*10^(n/2))+1. For n odd, either a(n) = floor(Pi*sqrt(10/3)*10^((n-1)/2)) or a(n) = floor(Pi*sqrt(10/3)*10^((n-1)/2))+1.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..30

Prog

(Python)
from sympy import totient
def A343802(n):
    s, c = 0, 0
    while s < 10**n:
        c += 1
        s += totient(c)
    return c

Crossrefs

Cf. A002088, A038567.

Sequence in context: A093374 A258109 A000745 * A271014 A272583 A247717

Adjacent sequences: A343799 A343800 A343801 * A343803 A343804 A343805

Keyword

nonn

Author

Chai Wah Wu, Apr 29 2021

Status

approved