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A223175 Smallest prime q such that 2n+1 = p + 8*q for some odd prime p, or 0 if no such prime exists.

%I A223175 #17 May 13 2013 00:15:30
%S A223175 0,0,0,0,0,0,0,0,0,2,2,2,0,2,2,3,2,2,3,2,3,3,2,2,0,5,2,3,2,2,3,2,3,3,
%T A223175 2,3,7,2,2,7,5,2,3,2,2,3,5,2,3,2,5,3,2,3,7,5,2,7,2,2,3,2,2,3,2,3,3,7,
%U A223175 3,7,5,2,7,2,5,3,2,2,7,7,3,3,2,2,7,5,2
%N A223175 Smallest prime q such that 2n+1 = p + 8*q for some odd prime p, or 0 if no such prime exists.
%C A223175 For n > 8, a(12) = a(24) = 0.
%C A223175 The corresponding p: 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 7, 0, 11, 13, 7, 17, 19, 13, 23, 17, 19, 29, 31, 0, 11,... are not always the minimum values. The smallest primes p are in A223174.
%C A223175 Conjecture: except m = 25 and 49, all odd numbers > 17 are of the form m = p + 8*q where p and q are prime numbers.
%H A223175 Michel Lagneau, <a href="/A223175/b223175.txt">Table of n, a(n) for n = 0..10000</a>
%e A223175 a(14) = 2 because, for q=2 the corresponding p=13 and 13+8*2 = 29 is prime.
%p A223175 for n from 1 by 2 to 200 do:jj:=0:for j from 1 to 1000 while (jj=0) do:q:=ithprime(j):p:=n-8*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 A223175 Cf. A219252, A219254, A219604, A219252, A223174, A103506.
%K A223175 nonn
%O A223175 0,10
%A A223175 _Michel Lagneau_, May 09 2013