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A047949 a(n) = largest m such that n-m and n+m are both primes, or -1 if no such m exists. 6
0, 0, 1, 2, 1, 4, 5, 4, 7, 8, 7, 10, 9, 8, 13, 14, 13, 12, 17, 16, 19, 20, 19, 22, 21, 20, 25, 24, 23, 28, 29, 28, 27, 32, 31, 34, 35, 34, 33, 38, 37, 40, 39, 38, 43, 42, 41, 30, 47, 46, 49, 50, 49, 52, 53, 52, 55, 54, 53, 48, 51, 50, 45, 62, 61, 64, 63, 62, 67, 68, 67, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

A067076 is a subsequence of this sequence: when 2m+3 is prime a(m+3) = m. Moreover, it is the subsequence of records (maximal increasing subsequence): let m=a(n), with p=n-m and q=p+2m both odd primes > 3; now 3+2(m+(p-3)/2)=q and hence a(3+m+(p-3)/2) >= m+(p-3)/2 > m = a(n) but 3+m+(p-3)/2 < n. - Jason Kimberley, Aug 30 2012 and Oct 10 2012

Goldbach's conjecture says a(n) >= 0 for all n. - Robert Israel, Apr 15 2015

LINKS

T. D. Noe, Table of n, a(n) for n=2..10000

OEIS (Plot 2), A067076 vs A098090 (n-m=3). - Jason Kimberley, Oct 01 2012

FORMULA

a(n) = n - A020481(n).

a(n) = (A020482(n) - A020481(n))/2. - Gionata Neri, Apr 15 2015

EXAMPLE

49-30=19 and 49+30=79 are primes, so a(49)=30.

MAPLE

a:= proc(n)

local k;

  for k from n - 1 to 0 by -2 do

     if isprime(n+k) and isprime(n-k) then return(k) fi

od:

-1

end proc:

0, seq(a(n), n=3..1000); # Robert Israel, Apr 16 2015

MATHEMATICA

a[2] = a[3] = 0; a[n_] := (For[m = n - 2, m >= 0, m--, If[PrimeQ[n - m] && PrimeQ[n + m], Break[]]]; m); Table[a[n], {n, 2, 100}] (* Jean-Fran├žois Alcover, Sep 04 2013 *)

lm[n_]:=Module[{m=n-2}, While[!AllTrue[n+{m, -m}, PrimeQ], m--]; m]; Join[{0, 0}, Array[ lm, 70, 4]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 03 2014 *)

PROG

(PARI) a(n) = {if (n==2 || n==3, return (0)); my(m = 1, lastm = -1, do = 1); while (do, if (isprime(n-m) && isprime(n+m), lastm = m); m++; if (m == n - 1, do = 0); ); return (lastm); } \\ Michel Marcus, Jun 09 2013

(PARI) a(n)=if(n<4, 0, forprime(p=3, n-1, if(isprime(2*n-p), return(n-p))); -1) \\ Ralf Stephan, Dec 29 2013

(Haskell)

a047949 n = if null qs then -1 else head qs  where

   qs = [m | m <- [n, n-1 .. 0], a010051' (n+m) == 1, a010051' (n-m) == 1]

-- Reinhard Zumkeller, Nov 02 2015

CROSSREFS

Cf. A047160, A067076, A182138.

Cf. A020481.

Cf. A010051.

Sequence in context: A165050 A165042 A165046 * A222986 A222906 A197011

Adjacent sequences:  A047946 A047947 A047948 * A047950 A047951 A047952

KEYWORD

easy,nice,nonn

AUTHOR

Lior Manor

EXTENSIONS

Corrected by Harvey P. Dale, Dec 21 2000

STATUS

approved

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Last modified March 28 05:07 EDT 2017. Contains 284182 sequences.