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A219252 Smallest prime q such that 2*n+1 = p + 4*q for some odd prime p, otherwise 0 if no such q exists.

%I A219252 #25 Apr 12 2013 15:32:23
%S A219252 0,0,0,0,2,2,2,3,2,2,3,2,2,3,2,5,3,2,2,3,3,2,7,2,2,3,2,5,3,2,5,3,2,2,
%T A219252 3,3,2,0,2,2,3,3,2,7,2,5,3,2,5,3,5,2,7,2,2,3,2,2,3,2,5,3,5,5,7,5,2,7,
%U A219252 2,7,3,2,2,3,3,11,7,2,2,3,3,2,7,3,2,19,2,5,3,2
%N A219252 Smallest prime q such that 2*n+1 = p + 4*q for some odd prime p, otherwise 0 if no such q exists.
%C A219252 a(38) = 0.
%C A219252 Conjecture: except m = 77, all odd number > 9 are of the form m = p + 4*q where p and q are prime numbers.
%H A219252 Michel Lagneau, <a href="/A219252/b219252.txt">Table of n, a(n) for n = 1..10000</a>
%e A219252 3 + 4*2 = 11 => a(5) = 2;
%e A219252 5 + 4*2 = 13 => a(6) = 2;
%e A219252 7 + 4*2 = 15 => a(7) = 2;
%e A219252 5 + 4*3 = 17 => a(8) = 3.
%p A219252 for n from 11 by 2 to 200 do:jj:=0:for j from 1 to 1000 while (jj=0) do:q:=ithprime(j):p:=n-4*q:if p> 0 and type(p,prime)=true  then jj:=1:printf(`%d, `,q):else fi:od:if jj=0 then printf(`%d, `,0):else fi:od:
%Y A219252 Cf. A195352, A002091, A219254.
%K A219252 nonn
%O A219252 1,5
%A A219252 _Michel Lagneau_, Apr 11 2013