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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A175161 A045875 A046434 * A205187 A162819 A029720

Adjacent sequences: A111043 A111044 A111045 * A111047 A111048 A111049

Keyword

easy,nonn

Author

Giovanni Teofilatto, Oct 06 2005

Extensions

Edited and extended by Ray Chandler, Oct 12 2005

Status

approved