login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A347310 a(n) = smallest k such that Sum_{i=1..k} log(p_i)/p_i >= n, where p_i is the i-th prime. 1
3, 8, 19, 43, 100, 236, 562, 1354, 3300, 8119, 20136, 50302, 126451, 319628, 811829, 2070790, 5302162, 13621745, 35101258, 90696900, 234924747, 609864582, 1586430423 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Suggested by Mertens's theorem that Sum_{p <= x} log(p)/p = log(x) + O(1).
REFERENCES
Tenenbaum, G. (2015). Introduction to analytic and probabilistic number theory, 3rd ed., American Mathematical Soc. See page 16.
LINKS
FORMULA
a(n) = pi(A347311(n)) = A000720(A347311(n)). - Michel Marcus, Sep 06 2021
EXAMPLE
a(1) = 3 because log(2)/2 + log(3)/3 + log(5)/5 = 1.034665268989... is the first time the sum is >= 1.
MATHEMATICA
Table[k=1; While[Sum[Log@Prime@i/Prime@i, {i, ++k}]<n]; k, {n, 8}] (* Giorgos Kalogeropoulos, Sep 08 2021 *)
PROG
(PARI) a(n) = my(k=0, s=0, p=2); while (s < n, s += log(p)/p; k++; p = nextprime(p+1)); k; \\ Michel Marcus, Sep 06 2021
CROSSREFS
Sequence in context: A054480 A371796 A191787 * A332719 A326599 A121551
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Sep 06 2021
EXTENSIONS
a(8)-a(16) from Michel Marcus, Sep 06 2021
a(17)-a(23) from Jon E. Schoenfield, Sep 06 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)