A219604 Smallest prime p such that 2n+1 = 4q + p for some odd prime q, or 0 if no such prime exists.

0, 0, 0, 0, 3, 5, 3, 5, 7, 13, 3, 5, 7, 17, 3, 5, 7, 17, 11, 13, 23, 17, 3, 5, 7, 41, 3, 5, 7, 17, 11, 13, 23, 17, 3, 5, 7, 0, 3, 5, 7, 17, 11, 13, 23, 17, 3, 5, 7, 73, 11, 13, 31, 17, 19, 37, 23, 41, 3, 5, 7, 73, 3, 5, 7, 17, 11, 13, 23, 17, 19, 29, 23, 73, 3

Offset: 1

Author

Michel Lagneau, Apr 12 2013

Keywords

• nonn

Comments

a(38) = 0.

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

Links

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

Crossrefs

Cf. A219252, A219254, A103506.

Programs

Maple

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

Mathematica

Table[m=3;While[!(PrimeQ[m]&&(((2*n+1-m)/4)>1)&&PrimeQ[(2*n+1-m)/4]),m=m+2];Print[n," ",m],{n,5,200}]