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%I #19 Oct 14 2023 13:18:46
%S 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,
%T 28,29,26,31,32,35,30,33,34,37,39,38,40,41,36,42,43,45,46,48,51,49,54,
%U 57,44,47,50,52,55,58,59,53,61,62,65,60,63,64,67,69,56,68,70,71,73,74
%N The Goldbach permutation: take A065305, cross out repetitions and subtract 2 from each term.
%C 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.
%H Reinhard Zumkeller, <a href="/A065306/b065306.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t 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 *)
%o (Haskell)
%o a065306 n = a065306_list !! (n-1)
%o a065306_list = map (subtract 2) $ f (concat a065305_tabl) [] where
%o f (x:xs) ys = if x `elem` ys then f xs ys else x : f xs (x:ys)
%o -- _Reinhard Zumkeller_, Jan 30 2012
%Y A065305, A065307.
%Y Cf. A205666 (fixed points).
%K nice,nonn
%O 1,2
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 29 2001