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

1,1

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

Formula

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

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

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 *)

Prog

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

Crossrefs

Cf. A075321, A075323.

Sequence in context: A106068 A304875 A164566 * A079850 A065995 A023245

Adjacent sequences: A075319 A075320 A075321 * A075323 A075324 A075325

Keyword

nonn

Author

Amarnath Murthy, Sep 14 2002

Extensions

Corrected by R. J. Mathar, Nov 26 2014

Status

approved