A065307 -id:A065307 - cp's OEIS frontend

A205666 Fixed points of permutations A065306 and A065307.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 19, 38, 42, 43, 55, 63, 64, 68, 75, 76, 86, 106, 107, 108, 109, 112, 113, 120, 131, 156, 157, 175, 185, 194, 233, 270, 301, 369, 380, 438, 443, 470, 531, 663, 760, 803, 810, 847, 871, 934, 999, 1021, 1044

Offset: 1

Reinhard Zumkeller, Jan 30 2012

nonn

A065306(a(n)) = a(n); A065307(a(n)) = a(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..500

a205666 n = a205666_list !! (n-1)
a205666_list = [x | x <- [1..], a065306 x == fromIntegral x]
-- Reinhard Zumkeller, Jan 30 2012

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

Original entry on oeis.org

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

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

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.

A065305, A065307.

Cf. A205666 (fixed points).

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

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 *)

cp's OEIS Frontend

A205666 Fixed points of permutations A065306 and A065307.

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