login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047949 a(n) is the largest m such that n-m and n+m are both primes, or -1 if no such m exists. 7
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

a(n) is the Goldbach partition of 2n which results in the maximum spread divided by 2. - Robert G. Wilson v, Jun 18 2018

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-François 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 *)

f[n_] := Block[{q = 2}, While[q <= n && !PrimeQ[2n -q], q = NextPrime@ q]; n - q]; Array[f, 72, 2] (* Robert G. Wilson v, Jun 18 2018 *)

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 A323955

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 18:50 EST 2021. Contains 349424 sequences. (Running on oeis4.)