This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338994 #15 Feb 21 2021 02:10:09
%S A338994 2,20,21,19,19,20,15,18,10,16,10,18,18,10,11,10,9,14,9,16,11,8,9,17,
%T A338994 14,15,16,9,14,15,17,17,14,15,15,11,14,14,8,17,9,14,9,15,11,8,14,14,
%U A338994 13,9,9,13,15,15,9,13,15,14,13,8,9,9,14,15,15,14,8,12,8,13,16,8,9,13,14,9,7,9,9,15,8
%N A338994 Table read by antidiagonals: if x(n+1) = A001414(x(n-1)) + A001414(x(n)) with x(0) = i and x(1) = j, then T(i,j) is the first k such that (x(k), x(k+1)) is a fixed point or a member of a cycle. If there is no such k, then T(i,j) = -1.
%C A338994 The fixed points are (0,0) and (16,16) (i.e., if x(0)=16 and x(1)=16 then all x(n)=16). Cycles include (23, 32, 33, 24), (19, 28, 30, 21, 20), and (23, 34, 42, 31, 43, 74, 82, 82, 86, 88, 62, 50, 45).
%C A338994 Are there other cycles? Is T(i,j) ever -1? For 1 <= i <= 3000 and 1 <= j <= 3000, T(i,j) is never -1 and no other cycles are encountered.
%H A338994 Robert Israel, <a href="/A338994/b338994.txt">Table of n, a(n) for n = 1..10011</a> (first 141 antidiagonals, flattened)
%e A338994 Table begins
%e A338994 2, 20, 19, 15, 10, 10, 8, 14, 14, 8, 13, 8, ...
%e A338994 21, 19, 18, 18, 9, 9, 15, 14, 14, 15, 12, 15, ...
%e A338994 20, 10, 18, 14, 17, 17, 8, 14, 14, 8, 8, 8, ...
%e A338994 16, 10, 9, 14, 17, 17, 13, 13, 13, 13, 12, 13, ...
%e A338994 11, 16, 15, 14, 9, 9, 8, 16, 16, 8, 12, 8, ...
%e A338994 11, 16, 15, 14, 9, 9, 8, 16, 16, 8, 12, 8, ...
%e A338994 9, 15, 9, 13, 9, 9, 7, 14, 14, 7, 12, 7, ...
%e A338994 11, 15, 15, 14, 13, 13, 12, 13, 13, 12, 15, 12, ...
%e A338994 11, 15, 15, 14, 13, 13, 12, 13, 13, 12, 15, 12, ...
%e A338994 9, 15, 9, 13, 9, 9, 7, 14, 14, 7, 12, 7, ...
%e A338994 14, 7, 6, 6, 23, 23, 4, 16, 16, 4, 12, 4, ...
%e A338994 9, 15, 9, 13, 9, 9, 7, 14, 14, 7, 12, 7, ...
%e A338994 T(1,7) = 8 because starting at x(0)=1, x(1)=7 we have x(2)=7, x(3)=14, x(4)=16, x(5)=17, x(6)=25, x(7)=27, x(8)=19, x(9)=28, and (19,28) is in the cycle (19, 28, 30, 21, 20).
%p A338994 spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A338994 Cyc:= {[0, 0], [16, 16], [32, 33], [33, 24], [24, 23], [23, 32], [28, 30], [30, 21], [21, 20], [20, 19], [19, 28], [34, 42], [42, 31], [31, 43], [43, 74], [74, 82], [82, 82], [82, 86], [86, 88], [88, 62], [62, 50], [50, 45], [45, 23], [23, 34]}:
%p A338994 f:= proc(t) local count,x;
%p A338994 count:= 0;
%p A338994 x:= t;
%p A338994 while count < 1000 do
%p A338994 if member(x,Cyc) then return count fi;
%p A338994 x:= [x[2],spf(x[1])+spf(x[2])];
%p A338994 count:= count+1;
%p A338994 od;
%p A338994 FAIL
%p A338994 end proc:
%p A338994 seq(seq(f([i,k-i]),i=1..k-1),k=2..14);
%Y A338994 Cf. A001414, A338937.
%K A338994 nonn,tabl
%O A338994 1,1
%A A338994 _J. M. Bergot_ and _Robert Israel_, Nov 17 2020