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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 (list; graph; refs; listen; history; text; internal format)
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

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

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-Fran├žois Alcover, Feb 12 2018, translated from R. J. Mathar's program *)

PROG

(Haskell)

a075321 = a075323 . subtract 1 . (* 2)

-- Reinhard Zumkeller, Nov 29 2014

CROSSREFS

Cf. A075322, A075323.

Sequence in context: A101301 A103116 A303853 * A258030 A164787 A131205

Adjacent sequences:  A075318 A075319 A075320 * A075322 A075323 A075324

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 14 2002

EXTENSIONS

Corrected by R. J. Mathar, Nov 26 2014

STATUS

approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)