A223174 Smallest prime p such that 2n+1 = p + 8*q for some odd prime q, or 0 if no such prime exists.

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

Offset

0,10

Comments

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

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.

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) = 5 because, for p=5 the corresponding q=3 and 5+8*3 = 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: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:

Crossrefs

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

Sequence in context: A099744 A024601 A173013 * A225401 A085090 A084713

Adjacent sequences: A223171 A223172 A223173 * A223175 A223176 A223177

Keyword

nonn

Author

Michel Lagneau, May 09 2013

Status

approved