A075323 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), ... This lists the successive pairs in order.
3, 5, 7, 11, 13, 19, 23, 31, 37, 47, 17, 29, 53, 67, 43, 59, 61, 79, 83, 103, 109, 131, 73, 97, 101, 127, 139, 167, 41, 71, 149, 181, 157, 191, 137, 173, 113, 151, 193, 233, 197, 239, 179, 223, 211, 257, 229, 277, 263, 313, 199
Offset: 1
Keywords
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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Haskell
import Data.List ((\\)) a075323 n = a075323_list !! (n-1) a075323_list = f 1 [] $ tail a000040_list where f k ys qs = g qs where g (p:ps) | a010051' pk == 0 || pk `elem` ys = g ps | otherwise = p : pk : f (k + 1) (p:pk:ys) (qs \\ [p, pk]) where pk = p + 2 * k -- Reinhard Zumkeller, Nov 29 2014 -
Maple
# A075321p implemented in A075321 A075323 := proc(n) if type(n,'odd') then op(1,A075321p((n+1)/2)) ; else op(2,A075321p(n/2)) ; end if; end proc: seq(A075323(n),n=1..60) ; # R. J. Mathar, Nov 26 2014
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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}]]]]]; A075323[n_] := If[OddQ[n], A075321p[(n+1)/2][[1]], A075321p[n/2][[2]]]; Array[A075323, 50] (* Jean-François Alcover, Feb 12 2018, after R. J. Mathar *)
Extensions
Corrected by R. J. Mathar, Nov 26 2014
Comments