login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A200474 Floor(10*(prime(n+1)-prime(n))/log(prime(n))^2). 2
3, 6, 2, 4, 6, 1, 5, 3, 1, 2, 4, 3, 1, 3, 2, 1, 3, 2, 3, 3, 1, 0, 1, 0, 1, 6, 1, 2, 0, 4, 0, 2, 2, 1, 2, 2, 0, 3, 0, 1, 0, 4, 4, 1, 0, 1, 2, 0, 3, 1, 1, 1, 0, 1, 1, 0, 3, 4, 1, 0, 1, 4, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 0, 1, 1, 1, 2, 1, 0, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

COMMENTS

Cramer's conjecture is true if, for every n >= 5, a(n) is smaller than 10.

If Cramer's conjecture is true, then Andrica's conjecture is true. [John W. Nicholson, Feb 06 2012]

Some mathematicians are trying to prove: if Andrica's conjecture is true, then Cramer's conjecture is true. [Arkadiusz Wesolowski, Feb 22 2012]

LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 5..10000

Carlos Rivera, Conjecture 7

Eric Weisstein's World of Mathematics, Cramer Conjecture

FORMULA

a(n) = floor(10*A001223(n)/log(A000040(n))^2), n >= 5.

EXAMPLE

a(9) = 6 because 10*(29-23)/log(23)^2 = 6.1029419977....

MATHEMATICA

Table[Floor[10*(Prime[n + 1] - Prime[n])/Log[Prime[n]]^2], {n, 5, 100}]

CROSSREFS

Cf. A000040, A001223, A086142, A124129, A200324.

Sequence in context: A019769 A092948 A308315 * A154858 A169837 A333010

Adjacent sequences:  A200471 A200472 A200473 * A200475 A200476 A200477

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Nov 18 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 3 12:37 EDT 2020. Contains 333197 sequences. (Running on oeis4.)