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

1,1

Links

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

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

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 *)

Prog

(Haskell)
a075369 = (^ 2) . a014574  -- Reinhard Zumkeller, Feb 10 2015
(PARI) p=2; forprime(b=3, 1e3, if(b-p==2, print1(b*p+1", ")); p=b) \\ Altug Alkan, Nov 10 2015
(Magma) [a: n in [1..300] | IsSquare(a) where a is NthPrime(n)*NthPrime(n+1)+1]; // Vincenzo Librandi, Nov 19 2015

Crossrefs

Cf. A014574, A037074, A120875.

Sequence in context: A229134 A069262 A076956 * A318425 A273373 A264546

Adjacent sequences: A075366 A075367 A075368 * A075370 A075371 A075372

Keyword

nonn

Author

Amarnath Murthy, Sep 20 2002

Status

approved