login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 01:40 EDT 2021. Contains 345404 sequences. (Running on oeis4.)