A065306 The Goldbach permutation: take A065305, cross out repetitions and subtract 2 from each term.

1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 11, 12, 13, 15, 14, 16, 17, 18, 19, 21, 22, 24, 27, 20, 23, 25, 28, 29, 26, 31, 32, 35, 30, 33, 34, 37, 39, 38, 40, 41, 36, 42, 43, 45, 46, 48, 51, 49, 54, 57, 44, 47, 50, 52, 55, 58, 59, 53, 61, 62, 65, 60, 63, 64, 67, 69, 56, 68, 70, 71, 73, 74

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 29 2001

Keywords

• nice
• nonn

Comments

The sequence would be a permutation of the naturals if Goldbach's conjecture holds (every even integer n greater than two is the sum of two primes). Inverse: A065307.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to Goldbach conjecture
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

A065305, A065307.

Cf. A205666 (fixed points).

Programs

Haskell

a065306 n = a065306_list !! (n-1)
a065306_list = map (subtract 2) $ f (concat a065305_tabl) [] where
   f (x:xs) ys = if x `elem` ys then f xs ys else x : f xs (x:ys)
-- Reinhard Zumkeller, Jan 30 2012

Mathematica

t[n_, k_] := (Prime[n] + Prime[k])/2; A065305 = Flatten[ Table[ t[n, k], {n, 2, 22}, {k, 2, n}]]; A065306 = (A065305 //. {a___, b_, c___, b_, d___} :> {a, b, c, d}) - 2 (* Jean-François Alcover, Jan 25 2012 *)