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 A284170 Array read by antidiagonals: T(i,j) is the largest prime in the sequence defined by a(1) = prime(i), a(2) = prime(j), a(n) = A006530(a(n-1)+a(n-2)+1) for n>=3, or 0 if that sequence contains arbitrarily large primes. 1
 5, 43, 43, 5, 43, 5, 7, 43, 43, 43, 43, 41, 131, 43, 43, 13, 43, 43, 43, 41, 13, 17, 43, 41, 43, 131, 43, 137, 43, 43, 131, 43, 43, 43, 43, 43, 23, 43, 137, 43, 131, 43, 41, 67, 151, 29, 43, 131, 43, 41, 131, 137, 131, 43, 29, 137, 41, 137, 41, 151, 43, 131, 43, 137, 73, 43, 37, 43, 43, 131, 43, 47 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A006530. Sequence in context: A216334 A132487 A178614 * A067927 A038546 A022891 Adjacent sequences:  A284167 A284168 A284169 * A284171 A284172 A284173 KEYWORD nonn,tabl AUTHOR Robert Israel, Mar 21 2017 STATUS approved

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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)