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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.
3
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
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
Sequence in context: A106068 A304875 A164566 * A079850 A065995 A023245
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 14 2002
EXTENSIONS
Corrected by R. J. Mathar, Nov 26 2014
STATUS
approved