OFFSET
1,2
COMMENTS
2 and 4 are the only even terms in the sequence. Is every odd positive integer in the sequence?
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
Of the positive integers not among the first 4 terms of the sequence, 7 is the smallest which is coprime to a(3) + a(4) = 4 + 5 = 9.
MAPLE
N:= 1000: # to get the first N terms
LCp:= proc(c, R, q)
local T, TM, m;
T:= select(t -> igcd(t, q) = 1, {$1 .. q-1});
m:= floor(c/q);
T:= map(`+`, T, m*q);
TM:= T minus R minus {$m*q .. c};
while TM = {} do
T:= map(`+`, T, q);
TM := T minus R;
od:
min(TM);
end proc;
c:= 1: R:= {2, 4, 5}:
for n from 5 to N do
if A110924[n] = c+2 then
c:= c+2;
while member(c+2, R) do c:= c+2 od:
R:= select(`>`, R, c);
else
R:= R union {A110924[n]}
fi;
od:
seq(A110924[n], n=1..N); # Robert Israel, May 09 2014
MATHEMATICA
a[1] = 1; a[2] = 2; a[3] = 4;
a[n_] := a[n] = Module[{aa = Array[a, n-1], b = a[n-1] + a[n-2]}, For[k = 3, True, k += 2, If[FreeQ[aa, k], If[CoprimeQ[k, b], Return[k]]]]];
Array[a, 100] (* Jean-François Alcover, Aug 26 2020 *)
PROG
(PARI) { 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, ", ")) } \\ Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Sep 23 2005
EXTENSIONS
More terms from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005
STATUS
approved