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

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, 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, 3, 7, 5, 2, 7, 2, 5, 3, 2, 2, 7, 7, 3, 3, 2, 2, 7, 5, 2

Offset: 0

Author

Michel Lagneau, May 09 2013

Keywords

• nonn

Comments

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

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.

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.

Examples

			a(14) = 2 because, for q=2 the corresponding p=13 and 13+8*2 = 29 is prime.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A219252, A219254, A219604, A219252, A223174, A103506.

Programs

Maple

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: