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

1,5

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.

Links

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

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}]

Crossrefs

Cf. A219252, A219254, A103506.

Sequence in context: A228446 A364564 A188889 * A296489 A253398 A151568

Adjacent sequences: A219601 A219602 A219603 * A219605 A219606 A219607

Keyword

nonn

Author

Michel Lagneau, Apr 12 2013

Status

approved