

A075323


Pair the odd primes so that the nth 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), ... This lists the successive pairs in order.


5



3, 5, 7, 11, 13, 19, 23, 31, 37, 47, 17, 29, 53, 67, 43, 59, 61, 79, 83, 103, 109, 131, 73, 97, 101, 127, 139, 167, 41, 71, 149, 181, 157, 191, 137, 173, 113, 151, 193, 233, 197, 239, 179, 223, 211, 257, 229, 277, 263, 313, 199
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OFFSET

1,1


COMMENTS

Question: Is every odd prime a member of some pair?
2683 = A065091(388) seems to be missing, as presumably A247233(388)=0; but if A247233(n) > 0: a(A247233(n)) = A065091(n) = A000040(n+1).  Reinhard Zumkeller, Nov 29 2014


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


MAPLE

# A075321p implemented in A075321
A075323 := proc(n)
if type(n, 'odd') then
op(1, A075321p((n+1)/2)) ;
else
op(2, A075321p(n/2)) ;
end if;
end proc:
seq(A075323(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}]]]]];
A075323[n_] := If[OddQ[n], A075321p[(n+1)/2][[1]], A075321p[n/2][[2]]];
Array[A075323, 50] (* JeanFrançois Alcover, Feb 12 2018, after R. J. Mathar *)


PROG

(Haskell)
import Data.List ((\\))
a075323 n = a075323_list !! (n1)
a075323_list = f 1 [] $ tail a000040_list where
f k ys qs = g qs where
g (p:ps)  a010051' pk == 0  pk `elem` ys = g ps
 otherwise = p : pk : f (k + 1) (p:pk:ys) (qs \\ [p, pk])
where pk = p + 2 * k
 Reinhard Zumkeller, Nov 29 2014


CROSSREFS

Cf. A075321, A075322.
Cf. A010051, A000040, A065091, A247233.
Sequence in context: A132779 A192869 A147513 * A020575 A055072 A059334
Adjacent sequences: A075320 A075321 A075322 * A075324 A075325 A075326


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Sep 14 2002


EXTENSIONS

Corrected by R. J. Mathar, Nov 26 2014


STATUS

approved



