A111046 Difference between squares of twin prime pairs.

16, 24, 48, 72, 120, 168, 240, 288, 408, 432, 552, 600, 720, 768, 792, 912, 960, 1080, 1128, 1248, 1392, 1680, 1728, 1848, 2088, 2280, 2400, 2472, 2568, 2640, 3240, 3288, 3312, 3432, 3528, 4080, 4128, 4200, 4248, 4368, 4608, 4920, 5112, 5160, 5208, 5280

Offset: 1

Author

Giovanni Teofilatto, Oct 06 2005

Keywords

• easy
• nonn

Comments

Except for the first term 16 = 4^2, a(n) is never a square.

Links

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

Crossrefs

Cf. A001359, A006512, A014574, A040040, A054735, A108570, A108604.

Programs

Haskell

a111046 = (* 2) . a054735  -- Reinhard Zumkeller, Feb 10 2015

Maple

ZL:=[]:for p from 1 to 1400 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL),(((p+2)^2)-p^2)]; fi; od; print(ZL); # Zerinvary Lajos, Mar 08 2007

Mathematica

Select[Table[Prime[n] + 1, {n, 220}], PrimeQ[ # + 1] &] *4 (* Ray Chandler, Oct 12 2005 *)
4+4#&/@Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]]==2&] [[All,1]] (* Harvey P. Dale, Apr 12 2018 *)

Formula

a(n) = A006512(n)^2 - A001359(n)^2 = A108604(n) - A108570(n) = 2*A054735(n) = 4*A014574(n) = 8*A040040(n).

Extensions

Edited and extended by Ray Chandler, Oct 12 2005