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

1,2

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

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 *)

Prog

(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

Crossrefs

A065305, A065307.

Cf. A205666 (fixed points).

Sequence in context: A304481 A222254 A235489 * A065307 A356759 A367935

Adjacent sequences: A065303 A065304 A065305 * A065307 A065308 A065309

Keyword

nice,nonn

Author

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

Status

approved