The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A200654 Smallest k>0 such that k*p*(k*p+1)-1 and k*p*(k*p+1)+1 are twin primes, where p = n-th prime. 2
1, 1, 1, 3, 6, 27, 9, 2, 6, 7, 5, 14, 1, 5, 3, 10, 1, 15, 93, 36, 33, 5, 18, 1, 18, 1, 2, 28, 2, 10, 8, 1, 34, 11, 12, 3, 2, 116, 4, 52, 31, 29, 18, 42, 13, 32, 24, 71, 93, 122, 61, 75, 11, 141, 73, 31, 57, 36, 23, 43, 18, 15, 69, 33, 15, 10, 39, 8, 108, 29, 72, 7, 8, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
(Sum_{n=1..N} k) / (Sum_{n=1..N} log(p)^2) tends to 1 as N increases.
LINKS
EXAMPLE
1*2*(1*2 + 1) - 1 = 5 and 1*2*(1*2 + 1) + 1 = 7;
5 and 7 are twin primes, so a(1)=1 as p(1)=2.
1*3*(1*3 + 1) - 1 = 11 and 1*3*(1*3 + 1) + 1 = 13;
11 and 13 are twin primes, so a(2)=1 as p(2)=3.
MAPLE
A200654 := proc(n)
p := ithprime(n) ;
for k from 1 do
if isprime(k*p*(k*p+1)-1) and isprime(k*p*(k*p+1)+1) then
return k;
end if;
end do:
return 0 ;
end proc:
seq(A200654(n), n=1..80) ; # R. J. Mathar, Nov 26 2011
CROSSREFS
Cf. A200778.
Sequence in context: A033194 A304051 A128437 * A208665 A256762 A064283
KEYWORD
nonn
AUTHOR
Pierre CAMI, Nov 20 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 16:30 EDT 2024. Contains 372801 sequences. (Running on oeis4.)