A092939 -id:A092939 - cp's OEIS frontend

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

Amarnath Murthy, Mar 23 2004

nonn

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.

			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.

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

Cf. A092939, A092940, A116619.

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

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 *)

{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

Edited and extended by Klaus Brockhaus, Dec 23 2006

A092940 a(n) = largest prime p such that 2*prime(n) - p is prime.

Original entry on oeis.org

2, 3, 7, 11, 19, 23, 31, 31, 43, 53, 59, 71, 79, 83, 89, 103, 113, 109, 131, 139, 139, 151, 163, 173, 191, 199, 199, 211, 211, 223, 251, 257, 271, 271, 293, 283, 311, 313, 331, 317, 353, 359, 379, 383, 389, 379, 419, 443, 449, 439, 463, 467, 479, 499, 509, 523

Offset: 1

Amarnath Murthy, Mar 23 2004

nonn

a(n) = largest prime p such that prime(n) = (p+q)/2, where q is also prime.
prime(n) <= a(n) < 2*prime(n).
Conjecture: a(n) = prime(n) only for n = 1 and 2.

			2*prime(18) = 122; the primes smaller than 122 are 113, 109, 107, ... in descending order. 122 - 113 = 9 is not prime, but 122 - 109 = 13 is prime, hence a(18) = 109.

Cf. A092938, A092939, A116619.

{for(n=1,56,k=2*prime(n);q=2;while(!isprime(p=k-q),q=nextprime(q+1));print1(p,","))} \\ Klaus Brockhaus, Dec 23 2006

a(n) = 2*prime(n) - A092938(n).

Edited and extended by Klaus Brockhaus, Dec 23 2006

cp's OEIS Frontend

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

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