A075369 Square associated with twin primes (p,p+2): p(p+2) + 1. Square of the average of twin primes.

16, 36, 144, 324, 900, 1764, 3600, 5184, 10404, 11664, 19044, 22500, 32400, 36864, 39204, 51984, 57600, 72900, 79524, 97344, 121104, 176400, 186624, 213444, 272484, 324900, 360000, 381924, 412164, 435600, 656100, 675684, 685584, 736164

Offset: 1

Author

Amarnath Murthy, Sep 20 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A014574, A037074, A120875.

Programs

Haskell

a075369 = (^ 2) . a014574  -- Reinhard Zumkeller, Feb 10 2015

Magma

[a: n in [1..300] | IsSquare(a) where a is NthPrime(n)*NthPrime(n+1)+1]; // Vincenzo Librandi, Nov 19 2015

Maple

P:= select(isprime,{seq(2*i+1,i=1..1000)}):
T:= P intersect map(`+`,P,2):
sort(convert(map(t -> (t-1)^2, T), list)); # Robert Israel, Nov 18 2015

Mathematica

f[n_]:=Prime[n]*Prime[n+1]+1; lst={}; Do[If[IntegerQ[Sqrt[f[n]]],AppendTo[lst,f[n]]],{n,4*5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 10 2010 *)

PARI

p=2; forprime(b=3, 1e3, if(b-p==2, print1(b*p+1", ")); p=b) \\ Altug Alkan, Nov 10 2015

Formula

a(n) = A037074(n) + 1. - Jon E. Schoenfield, Jan 13 2015

a(n) = A014574(n)^2. - Jon E. Schoenfield, Jan 14 2015

a(n) = A120875(n) + 2. - Jason Kimberley, Oct 22 2015