A075322 Pair the odd primes so that the k-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), ... This is the sequence of the second member of every pair.

5, 11, 19, 31, 47, 29, 67, 59, 79, 103, 131, 97, 127, 167, 71, 181, 191, 173, 151, 233, 239, 223, 257, 277, 313, 251, 281, 163, 389, 353, 373, 347, 307, 337, 419, 431, 457, 443, 479, 397, 461, 523, 577, 509, 499, 541, 557, 563

Offset: 1

Author

Amarnath Murthy, Sep 14 2002

Keywords

• nonn

Comments

Question: Is every prime p a member of some pair?

a(n) = A075323(2*n).

Links

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

Crossrefs

Cf. A075321, A075323.

Programs

Haskell

a075322 = a075323 . (* 2)  -- Reinhard Zumkeller, Nov 29 2014

Maple

# A075321p() implemented in A075321.
A075322 := proc(n)
    op(2,A075321p(n)) ;
end proc:
seq(A075322(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}]]]]];
a[n_] := A075321p[n][[2]];
Array[a, 50] (* Jean-François Alcover, Feb 12 2018, after R. J. Mathar *)

Formula

a(n) = A075321(n)+2*n.

a(n) = A075323(2*n).

Extensions

Corrected by R. J. Mathar, Nov 26 2014