GCD(a(n),a(n-1)+a(n-2))=1

[Lambert Klasen]

Dear Leroy,

> I am suprised this sequence is not in the EIS. Did I make a mistake in 
> calculating the terms by hand?
no! it goes on like this:
1,2,4,5,7,11,13,17,19,23,25,29,31,37,3,9,35,15,21,41,27,33,43,39,45,47,49,
53,55,59,61,67,51,57,65,63,69,71,73,77,79,83,85,89,91,97,75,81,95,87,93,
101,99,103,105,107,109,113,115,119,121,127,111,117,125,123,129,131,133,
137,139,143,145,149,151,157,135,141,155,147,153,161,159,163,165,167,169,
173,175,179,181,187,171,177,185,183,189,191,193,197,199,203,...

some ugly, optimizable pari code to create the sequence:
u=[2,1];
c=3;
s=u[1]+u[2];
m=Set()
m=setunion(m,[1]);
m=setunion(m,[2]);
print1(1,",",2);
for(k=1,100,\
i=2;while(gcd(i,s)>1 || setsearch(m,i)!=0,i++);\
u[(c%2)+1] = i;\
c++;\
s=u[1]+u[2];\
m=setunion(m,[i]);\
print1(i,","))

> What I wonder is, is every odd positive integer in the sequence?
yes.

best regards
        Lambert

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