A078496 - OEIS

%I #14 Jan 01 2024 02:00:18

%S 5,7,7,11,11,11,13,17,13,19,17,17,19,23,19,31,23,23,31,29,29,31,29,31,

%T 37,41,31,43,41,37,37,41,41,43,47,41,43,53,43,67,47,47,61,53,53,61,53,

%U 59,61,59,61,67,59,61,73,71,61,79,71,67,67,71,71,73,83,71,73,83,73,79

%N Smallest prime p such that p>n and 2*n-p is also prime.

%C Suggested by Goldbach Conjecture.

%C Values of q from A143697. This follows from the factorization n^2-k^2 = (n-k)(n+k).

%H P. CAMI, <a href="/A078496/b078496.txt">Table of n, a(n) for n = 4..60000</a>

%F n>3 integer; a(n)=min{p: p>n; p, 2*n-p are primes}.

%e a(11)=17.

%t Table[p=n+1; q=2n-p; While[q>0&&!(PrimeQ[p]&&PrimeQ[q]), p++; q-- ]; p, {n, 4, 100}]

%o (PARI) a(n) = {my(p=nextprime(n+1)); while(!isprime(2*n-p), p = nextprime(p+1)); p;} \\ _Michel Marcus_, Oct 22 2016

%Y Cf. A143697, A078587.

%Y a(n) = 2n - A078587(n).

%Y Cf. A082467

%K nonn

%O 4,1

%A Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), Nov 26 2002

%E Edited by _N. J. A. Sloane_, Jan 24 2009 at the suggestion of _R. J. Mathar_ and _T. D. Noe_.