%I #10 Jun 02 2022 11:24:42

%S 2,2,2,3,2,2,3,2,2,3,2,3,7,2,2,3,5,2,3,2,2,3,2,3,7,2,3,7,2,2,3,5,2,3,

%T 2,2,3,5,2,3,2,3,19,2,3,7,5,2,3,2,2,3,2,2,3,2,3,7,5,11,7,11,2,3,2,3,

%U 13,2,2,3,5,5,7,2,2,3,5,2,3,7,2,3,2,3,13

%N Smallest prime p such that 2*n+1 = 2*p + q for some odd prime q.

%C Related to Lemoine's conjecture, which states that all odd integers > 5 can be represented as 2*p+q, p, q primes.

%D See A002091.

%H Hugo Pfoertner, <a href="/A195352/b195352.txt">Table of n, a(n) for n = 3..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lemoine%27s_conjecture">Lemoine's conjecture</a>

%e a(3)=2 because 2*3+1=7=2*2+3; a(4)=2: 2*3+1=9=2*2+5; a(5)=2: 11=2*2+7; a(6)=3: 13=2*3+7.

%t spp[n_]:=Module[{p=2},While[CompositeQ[(2n+1)-2p],p=NextPrime[p]];p]; Array[ spp,90,3] (* _Harvey P. Dale_, Jun 02 2022 *)

%Y Cf. A002091, A103506 (smallest q), A046927, A195353 (positions of records), A195354 (records), A103153 (prime p=2 excluded), A185091.

%K nonn

%O 3,1

%A _Hugo Pfoertner_, Sep 16 2011