cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A138637 Products of prime quadruples.

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%I A138637 #9 Sep 10 2018 18:53:37
%S A138637 5005,46189,121330189,1445140189,463236778189,4862973196189,
%T A138637 12359548828189,18898278256189,112254342850189,144149198626189,
%U A138637 1022657400370189,7924420639216189,28604961973900189,59910402098980189
%N A138637 Products of prime quadruples.
%C A138637 Product of numbers n, n+2, n+6 and n+8 when are all prime. Quadruplet analog of A037074. Subset of A014613.
%H A138637 Harvey P. Dale, <a href="/A138637/b138637.txt">Table of n, a(n) for n = 1..1000</a>
%F A138637 a(n) = A007530(n)*A007530(n+2)*A007530(n+6)*A007530(n+8).
%p A138637 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
%t A138637 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 *)
%t A138637 Times@@@Select[Partition[Prime[Range[2500]],4,1],Differences[#]=={2,4,2}&] (* _Harvey P. Dale_, Sep 10 2018 *)
%Y A138637 Cf. A007530, A014613, A037074.
%K A138637 easy,nonn
%O A138637 1,1
%A A138637 _Jonathan Vos Post_, May 14 2008
%E A138637 More terms from _Stefan Steinerberger_ and _R. J. Mathar_, May 18 2008