A071700 Product of twin primes of form (4*k+3,4*(k+1)+1), k>=0.

15, 143, 3599, 5183, 11663, 32399, 36863, 51983, 57599, 97343, 121103, 176399, 186623, 359999, 435599, 685583, 1040399, 1065023, 1192463, 1327103, 1742399, 2039183, 2108303, 2214143, 2585663, 2624399, 2782223

Offset: 1

Author

Reinhard Zumkeller, Jun 04 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A037074, A071700 and of A182140.

Cf. A071697, a(n) = A071698(n)*A071699(n).

Programs

Haskell

a071700 n = a071700_list !! (n-1)
a071700_list = [x * y | x <- [3, 7 ..], a010051' x == 1,
                        let y = x + 2, a010051' y == 1]
-- Reinhard Zumkeller, Aug 05 2014

PARI

for(k=0,1e3,if(isprime(4*k+3)&&isprime(4*k+5),print1(16*k^2+32*k +15", "))) \\ Charles R Greathouse IV, Jul 03 2013

PARI

is(n)=my(k=sqrtint(n\16)); n==16*k^2+32*k+15 && isprime(4*k+3) && isprime(4*k+5) \\ Charles R Greathouse IV, Jul 03 2013

PARI

is(n)=my(t); n%16==15 && issquare(n+1,&t) && isprime(t-1) && isprime(t+1) \\ Charles R Greathouse IV, Dec 12 2016

PARI

list(lim)=my(v=List(),p=3); forprime(q=5,sqrtint(1+lim\1)+1, if(q-p==2 && p%4==3, listput(v,p*q)); p=q); Vec(v) \\ Charles R Greathouse IV, Dec 12 2016

Formula

a(n) >> n^2 log^4 n. - Charles R Greathouse IV, Jul 03 2013