

A200654


Smallest k>0 such that k*p*(k*p+1)1 and k*p*(k*p+1)+1 are twin primes, where p = nth 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

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:


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



