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

0,10

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.

Links

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

Example

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

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:

Crossrefs

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

Sequence in context: A036476 A104994 A118664 * A322213 A118205 A216265

Adjacent sequences: A223172 A223173 A223174 * A223176 A223177 A223178

Keyword

nonn

Author

Michel Lagneau, May 09 2013

Status

approved