

A065306


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


5



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
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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 (* JeanFrançois Alcover, Jan 25 2012 *)


PROG

(Haskell)
a065306 n = a065306_list !! (n1)
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: A031978 A222254 A235489 * A065307 A207334 A294660
Adjacent sequences: A065303 A065304 A065305 * A065307 A065308 A065309


KEYWORD

nice,nonn


AUTHOR

Klaus Strassburger (strass(AT)ddfi.uniduesseldorf.de), Oct 29 2001


STATUS

approved



