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A219252
Smallest prime q such that 2*n+1 = p + 4*q for some odd prime p, otherwise 0 if no such q exists.
6
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
1,5
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
EXAMPLE
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.
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:
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 11 2013
STATUS
approved