A092938 a(n) = least prime p such that 2*prime(n) - p is prime.

2, 3, 3, 3, 3, 3, 3, 7, 3, 5, 3, 3, 3, 3, 5, 3, 5, 13, 3, 3, 7, 7, 3, 5, 3, 3, 7, 3, 7, 3, 3, 5, 3, 7, 5, 19, 3, 13, 3, 29, 5, 3, 3, 3, 5, 19, 3, 3, 5, 19, 3, 11, 3, 3, 5, 3, 17, 19, 7, 5, 3, 17, 7, 3, 7, 3, 3, 13, 3, 7, 5, 17, 7, 3, 7, 5, 5, 7, 5, 7, 11, 3, 3, 3, 19, 3, 11, 3, 3, 7, 5, 5, 3, 5, 7, 23, 5, 3

Offset: 1

Author

Amarnath Murthy, Mar 23 2004

Keywords

• nonn

Comments

a(n) = least prime p such that prime(n) = (p+q)/2, where q is also prime.

a(n) <= prime(n). Conjecture: a(n) = prime(n) only for n = 1 and 2.

Examples

			2*prime(8) = 38; 38 - 2 = 36, 38 - 3 = 35, 38 - 5 = 33 are composite, but 38 - 7 = 31 is prime. Hence a(8) = 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A092939, A092940, A116619.

Programs

Maple

f:= proc(n) local pn,p;
   pn:= ithprime(n);
   p:= 1;
   do
     p:= nextprime(p);
     if isprime(2*pn-p) then return p fi
   od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 31 2020

Mathematica

a[n_] := Module[{p, q = Prime[n]}, For[p = 2, True, p = NextPrime[p], If[PrimeQ[2q-p], Return[p]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 07 2023 *)

PARI

{for(n=1, 98, k=2*prime(n); p=2; while(!isprime(k-p), p=nextprime(p+1)); print1(p,","))} \\ Klaus Brockhaus, Dec 23 2006

Extensions

Edited and extended by Klaus Brockhaus, Dec 23 2006