VOOZH about

URL: https://oeis.org/A075321

⇱ A075321 - OEIS

login
A075321
Pair the odd primes so that the n-th pair is (p, p+2n) where p is the smallest prime not included earlier such that p and p+2n are primes and p+2n also does not occur earlier: (3, 5), (7, 11), (13, 19), (23, 31), (37, 47), (17, 29), (53, 67) ... This is the sequence of the first member of every pair.
3
3, 7, 13, 23, 37, 17, 53, 43, 61, 83, 109, 73, 101, 139, 41, 149, 157, 137, 113, 193, 197, 179, 211, 229, 263, 199, 227, 107, 331, 293, 311, 283, 241, 269, 349, 359, 383, 367, 401, 317, 379, 439, 491, 421, 409, 449, 463, 467
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
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]];
Array[A075321, 50] (* Jean-François Alcover, Feb 12 2018, translated from R. J. Mathar's program *)
PROG
(Haskell)
a075321 = a075323 . subtract 1 . (* 2)
-- Reinhard Zumkeller, Nov 29 2014
CROSSREFS
Sequence in context: A101301 A103116 A303853 * A258030 A164787 A131205
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 14 2002
EXTENSIONS
Corrected by R. J. Mathar, Nov 26 2014
STATUS
approved