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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) MathOverflow, If p_n is the largest prime factor of p_{n-1}+p_{n-2}+m, then p_n is bounded 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: A132487 A178614 A360942 * 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 August 9 04:00 EDT 2024. Contains 375027 sequences. (Running on oeis4.)