OFFSET
1,1
COMMENTS
Conjecture: the sequence always eventually repeats, so T(i,j) > 0.
LINKS
Robert Israel, Table of n, a(n) for n = 1..14196 (first 168 antidiagonals, flattened)
EXAMPLE
T(1,2) = 43 because the sequence in this case starts 2,3,3,7,11,19,31,17,7, and then repeats 5,13,19,11,31,43,5,7,13,7,7 in a cycle.
Array starts
5 43 5 43 43 13 137 43 151 29 ...
43 43 43 43 41 43 43 67 43 73 ...
5 43 131 43 131 43 41 131 137 137 ...
7 41 43 43 43 43 137 43 131 67 ...
43 43 41 43 131 131 131 43 131 151 ...
13 43 131 43 41 43 43 43 73 73 ...
17 43 137 43 151 47 43 41 41 131 ...
43 43 131 41 43 41 43 41 67 137 ...
23 43 137 131 43 151 137 137 197 137 ...
29 41 43 137 73 43 131 41 131 389 ...
MAPLE
M:= 20: # to get the first M antidiagonals
with(queue):
backprop:= proc(r, p)
local t; global F;
for t in Parents[r] do
if F[t] < p then
F[t]:= p;
procname(t, p);
fi
od
end proc:
Verts:= {seq(seq([ithprime(i), ithprime(j)], i=1..M), j=1..M)}:
for v in Verts do F[v]:= max(v); Parents[v]:= {} od:
Agenda:= new(op(Verts)):
while not empty(Agenda) do
t:= dequeue(Agenda);
r:= [t[2], max(numtheory:-factorset(t[1]+t[2]+1))];
if member(r, Verts) then
Parents[r]:= Parents[r] union {t};
else
Verts:= Verts union {r};
Parents[r]:= {t};
enqueue(Agenda, r);
F[r]:= max(r);
fi;
backprop(r, F[r]);
od:
seq(seq(F[[ithprime(m-j), ithprime(j)]], j=1..m-1), m=2..M+1);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Robert Israel, Mar 21 2017
STATUS
approved