OFFSET
1,1
COMMENTS
Question: Is every prime a member of some pair?
If the distance between the prime pairs is not required to be 2n, we get A031215. - R. J. Mathar, Nov 26 2014
a(n) = A075323(2*n-1).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
EXAMPLE
a(4)=23: For the 4th pair though 17 is the smallest prime not occurring earlier, 17+8 = 25 is not a prime and 23 + 8 = 31 is a prime.
MAPLE
A075321p := proc(n)
option remember;
local prevlist, i, p, q ;
if n = 1 then
return [3, 5];
else
prevlist := [seq(op(procname(i)), i=1..n-1)] ;
for i from 2 do
p := ithprime(i) ;
if not p in prevlist then
q := p+2*n ;
if isprime(q) and not q in prevlist then
return [p, q] ;
end if;
end if;
end do:
end if;
end proc:
A075321 := proc(n)
op(1, A075321p(n)) ;
end proc:
seq(A075321(n), n=1..60) ; # R. J. Mathar, Nov 26 2014
MATHEMATICA
A075321p[n_] := A075321p[n] = Module[{prevlist, i, p, q }, If[n == 1, Return[{3, 5}], prevlist = Array[A075321p, n-1] // Flatten]; For[i = 2, True, i++, p = Prime[i]; If[FreeQ[prevlist, p], q = p + 2*n ; If[ PrimeQ[q] && FreeQ[ prevlist, q], Return[{p, q}]]]]];
A075321 [n_] := A075321p[n][[1]];
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 14 2002
EXTENSIONS
Corrected by R. J. Mathar, Nov 26 2014
STATUS
approved