%I
%S 0,0,0,0,3,5,3,5,7,13,3,5,7,17,3,5,7,17,11,13,23,17,3,5,7,41,3,5,7,17,
%T 11,13,23,17,3,5,7,0,3,5,7,17,11,13,23,17,3,5,7,73,11,13,31,17,19,37,
%U 23,41,3,5,7,73,3,5,7,17,11,13,23,17,19,29,23,73,3
%N Smallest prime p such that 2n+1 = 4q + p for some odd prime q, or 0 if no such prime exists.
%C a(38) = 0.
%C Conjecture: except m = 77, all odd number > 9 are of the form m = p + 4*q where p and q are prime numbers.
%H Michel Lagneau, <a href="/A219604/b219604.txt">Table of n, a(n) for n = 1..10000</a>
%p for n from 11 by 2 to 200 do:jj:=0:for j from 1 to 1000 while (jj=0) do:p:=ithprime(j):q:=(np)/4:if q> 0 and type(q,prime)=true then jj:=1:printf(`%d, `,p):else fi:od:if jj=0 then printf(`%d, `,0):else fi:od:
%t Table[m=3;While[!(PrimeQ[m]&&(((2*n+1m)/4)>1)&&PrimeQ[(2*n+1m)/4]),m=m+2];Print[n," ",m],{n,5,200}]
%Y Cf. A219252, A219254, A103506.
%K nonn
%O 1,5
%A _Michel Lagneau_, Apr 12 2013
