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Smallest prime p such that 2n+1 = p + 8*q for some odd prime q, or 0 if no such prime exists.
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%I #15 May 13 2013 00:16:36

%S 0,0,0,0,0,0,0,0,0,3,5,7,0,3,5,7,17,11,13,23,17,3,5,7,0,11,13,31,17,3,

%T 5,7,41,11,13,31,17,19,37,23,41,43,29,31,73,3,5,7,41,11,13,47,17,3,5,

%U 7,73,11,13,31,17,19,37,23,41,43,29,31,97,3,5,7,41

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

%C For n > 8, a(12) = a(24) = 0.

%C The corresponding q = 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 3, 3, 3, 2, 3, 3, 2, 3, 5, 5, 5, 0, 5, 5, 3, 5, 7, 7, 7,... are not always the minimum values. The smallest primes q are in A223175.

%C 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 Michel Lagneau, <a href="/A223174/b223174.txt">Table of n, a(n) for n = 0..10000</a>

%e a(14) = 5 because, for p=5 the corresponding q=3 and 5+8*3 = 29 is prime.

%p for n from 1 by 2 to 200 do:jj:=0:for j from 1 to 1000 while (jj=0) do:p:=ithprime(j):q:=(n-p)/8: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:

%Y Cf. A219252, A219254, A219604, A219252, A223175, A103506.

%K nonn

%O 0,10

%A _Michel Lagneau_, May 09 2013