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 A047160 For n >= 2, a(n) = smallest number m >= 0 such that n-m and n+m are both primes, or -1 if no such m exists. 18
 0, 0, 1, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 9, 0, 5, 6, 3, 4, 9, 0, 1, 0, 9, 4, 3, 6, 5, 0, 9, 2, 3, 0, 1, 0, 3, 2, 15, 0, 5, 12, 3, 8, 9, 0, 7, 12, 3, 4, 15, 0, 1, 0, 9, 4, 3, 6, 5, 0, 15, 2, 3, 0, 1, 0, 15, 4, 3, 6, 5, 0, 9, 2, 15, 0, 5, 12, 3, 14, 9, 0, 7, 12, 9, 4, 15, 6, 7, 0, 9, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,7 COMMENTS I have confirmed there are no -1 entries through integers to 4.29*10^9 using PARI. - Bill McEachen, Jul 07 2008 From Daniel Forgues, Jul 02 2009: (Start) Goldbach's Conjecture: for all n >= 2, there are primes (distinct or not) p and q s.t. p+q = 2n. The primes p and q must be equidistant (distance m >= 0) from n: p = n-m and q = n+m, hence p+q = (n-m)+(n+m) = 2n. Equivalent to Goldbach's Conjecture: for all n >= 2, there are primes p and q equidistant (distance >= 0) from n, where p and q are n when n is prime. If this conjecture is true, then a(n) will never be set to -1. Twin Primes Conjecture: there is an infinity of twin primes. If this conjecture is true, then a(n) will be 1 infinitely often (for which each twin primes pair is (n-1, n+1)). Since there is an infinity of primes, a(n) = 0 infinitely often (for which n is prime). (End) If n is composite, then n and a(n) are coprime, because otherwise n + a(n) would be composite. - Jason Kimberley, Sep 03 2011 LINKS T. D. Noe, Table of n, a(n) for n = 2..10000 J. S. Kimberley, Symmetrical plot of A047160 FORMULA a(n) = n - A112823(n). a(n) = A082467(n) * A005171(n), for n > 3. - Jason Kimberley, Jun 25 2012 EXAMPLE 16-3=13 and 16+3=19 are primes, so a(16)=3. MATHEMATICA Table[k = 0; While[k < n && (! PrimeQ[n - k] || ! PrimeQ[n + k]), k++]; If[k == n, -1, k], {n, 2, 100}] PROG (UBASIC) 10 N=2// 20 M=0// 30 if and{prmdiv(N-M)=N-M, prmdiv(N+M)=N+M} then print M; :goto 50// 40 inc M:goto 30// 50 inc N: if N>130 then stop// 60 goto 20 (MAGMA) A047160:=func; [A047160(n):n in[2..100]]; // Jason Kimberley, Sep 02 2011 (Haskell) a047160 n = if null ms then -1 else head ms             where ms = [m | m <- [0 .. n - 1],                             a010051' (n - m) == 1, a010051' (n + m) == 1] -- Reinhard Zumkeller, Aug 10 2014 (PARI) a(n)=forprime(p=n, 2*n, if(isprime(2*n-p), return(p-n))); -1 \\ Charles R Greathouse IV, Jun 23 2017 CROSSREFS Cf. A001031, A002092, A002372, A002373, A002374, A002375, A014092, A025583, A035026, A047949, A071406, A082467, A102084, A103147, A112823, A155764, A155765, A177461, A078611, A010051, A045917. Sequence in context: A319650 A285736 A325142 * A332497 A093347 A230409 Adjacent sequences:  A047157 A047158 A047159 * A047161 A047162 A047163 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Patrick De Geest, May 15 1999 Deleted a comment. - T. D. Noe, Jan 22 2009 Comment corrected and definition edited by Daniel Forgues, Jul 08 2009 STATUS approved

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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)