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 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. 1
 2, 20, 21, 19, 19, 20, 15, 18, 10, 16, 10, 18, 18, 10, 11, 10, 9, 14, 9, 16, 11, 8, 9, 17, 14, 15, 16, 9, 14, 15, 17, 17, 14, 15, 15, 11, 14, 14, 8, 17, 9, 14, 9, 15, 11, 8, 14, 14, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). 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. LINKS Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened) EXAMPLE Table begins 2, 20, 19, 15, 10, 10, 8, 14, 14, 8, 13, 8, ... 21, 19, 18, 18, 9, 9, 15, 14, 14, 15, 12, 15, ... 20, 10, 18, 14, 17, 17, 8, 14, 14, 8, 8, 8, ... 16, 10, 9, 14, 17, 17, 13, 13, 13, 13, 12, 13, ... 11, 16, 15, 14, 9, 9, 8, 16, 16, 8, 12, 8, ... 11, 16, 15, 14, 9, 9, 8, 16, 16, 8, 12, 8, ... 9, 15, 9, 13, 9, 9, 7, 14, 14, 7, 12, 7, ... 11, 15, 15, 14, 13, 13, 12, 13, 13, 12, 15, 12, ... 11, 15, 15, 14, 13, 13, 12, 13, 13, 12, 15, 12, ... 9, 15, 9, 13, 9, 9, 7, 14, 14, 7, 12, 7, ... 14, 7, 6, 6, 23, 23, 4, 16, 16, 4, 12, 4, ... 9, 15, 9, 13, 9, 9, 7, 14, 14, 7, 12, 7, ... 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). MAPLE spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc: 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]}: f:= proc(t) local count, x; count:= 0; x:= t; while count < 1000 do if member(x, Cyc) then return count fi; x:= [x[2], spf(x[1])+spf(x[2])]; count:= count+1; od; FAIL end proc: seq(seq(f([i, k-i]), i=1..k-1), k=2..14); CROSSREFS Cf. A001414, A338937. Sequence in context: A273466 A278938 A303157 * A217394 A072998 A024629 Adjacent sequences: A338991 A338992 A338993 * A338995 A338996 A338997 KEYWORD nonn,tabl AUTHOR J. M. Bergot and Robert Israel, Nov 17 2020 STATUS approved

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Last modified September 13 13:43 EDT 2024. Contains 375908 sequences. (Running on oeis4.)