A219252 Smallest prime q such that 2*n+1 = p + 4*q for some odd prime p, otherwise 0 if no such q exists.

0, 0, 0, 0, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 2, 2, 3, 3, 2, 7, 2, 2, 3, 2, 5, 3, 2, 5, 3, 2, 2, 3, 3, 2, 0, 2, 2, 3, 3, 2, 7, 2, 5, 3, 2, 5, 3, 5, 2, 7, 2, 2, 3, 2, 2, 3, 2, 5, 3, 5, 5, 7, 5, 2, 7, 2, 7, 3, 2, 2, 3, 3, 11, 7, 2, 2, 3, 3, 2, 7, 3, 2, 19, 2, 5, 3, 2

Offset: 1

Author

Michel Lagneau, Apr 11 2013

Keywords

• nonn

Comments

a(38) = 0.

Conjecture: except m = 77, all odd number > 9 are of the form m = p + 4*q where p and q are prime numbers.

Examples

			3 + 4*2 = 11 => a(5) = 2;
5 + 4*2 = 13 => a(6) = 2;
7 + 4*2 = 15 => a(7) = 2;
5 + 4*3 = 17 => a(8) = 3.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A195352, A002091, A219254.

Programs

Maple

for n from 11 by 2 to 200 do:jj:=0:for j from 1 to 1000 while (jj=0) do:q:=ithprime(j):p:=n-4*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: