A138637 Products of prime quadruples.

5005, 46189, 121330189, 1445140189, 463236778189, 4862973196189, 12359548828189, 18898278256189, 112254342850189, 144149198626189, 1022657400370189, 7924420639216189, 28604961973900189, 59910402098980189

Offset: 1

Author

Jonathan Vos Post, May 14 2008

Keywords

• easy
• nonn

Comments

Product of numbers n, n+2, n+6 and n+8 when are all prime. Quadruplet analog of A037074. Subset of A014613.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007530, A014613, A037074.

Programs

Maple

isA007530 := proc(n) local q; if isprime(n) and n>=5 then q := nextprime(n) ; if q-n = 2 then q := nextprime(q) ; if q -n = 6 then q := nextprime(q) ; RETURN( q-n = 8 ) ; else RETURN(false) ; fi ; else RETURN(false) ; ; fi ; else RETURN(false) ; ; fi ; end: A007530 := proc(n) option remember ; local a; if n = 1 then 5 ; else a := nextprime(A007530(n-1)) ; while not isA007530(a) do a := nextprime(a) ; od: RETURN(a) ; fi ; end: A138637 := proc(n) local p ; p := A007530(n) ; p*(p+2)*(p+6)*(p+8) ; end: seq(A138637(n),n=1..20) ; # R. J. Mathar, May 18 2008

Mathematica

a = {}; For[n = 1, n < 5000, n++, If[{Prime[n+1]-Prime[n], Prime[n+2]-Prime[n+1], Prime[n+3]-Prime[n+2]} == {2, 4, 2}, AppendTo[a, Prime[n]*Prime[n+1]*Prime[n+2]* Prime[n+3]]]]; a (* Stefan Steinerberger, May 18 2008 *)
Times@@@Select[Partition[Prime[Range[2500]],4,1],Differences[#]=={2,4,2}&] (* Harvey P. Dale, Sep 10 2018 *)

Formula

a(n) = A007530(n)*A007530(n+2)*A007530(n+6)*A007530(n+8).

Extensions

More terms from Stefan Steinerberger and R. J. Mathar, May 18 2008