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 A357554 Triangular array read by rows. For T(n,k) where 1 <= k <= n, start with x = k and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared, then that is T(n,k). 3
 1, 1, 2, 1, 2, 3, 1, 2, 2, 4, 1, 3, 3, 3, 5, 1, 2, 3, 3, 2, 6, 1, 4, 3, 4, 3, 4, 7, 1, 2, 4, 4, 4, 4, 2, 8, 1, 5, 3, 3, 5, 3, 3, 5, 9, 1, 2, 4, 4, 5, 5, 4, 4, 2, 10, 1, 6, 3, 5, 5, 6, 5, 5, 3, 6, 11, 1, 2, 3, 4, 4, 6, 6, 4, 4, 3, 2, 12, 1, 7, 5, 4, 5, 5, 7, 5, 5, 4, 5, 7, 13 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Robert Israel, Table of n, a(n) for n = 1..10011(rows 1 to 141, flattened) FORMULA If k divides n, or if k > sqrt(n) and k^2-n is divisible by k-1, then T(n,k) = k. T(n,2) = 2 if n is even, (n+1)/2 if n is odd. EXAMPLE For T(13,2) we have 2 -> floor(13/2) + (13 mod 2) = 7 -> floor(13/7) + (13 mod 7) = 7 so T(13,2) = 7. Triangle starts: 1; 1, 2; 1, 2, 3; 1, 2, 2, 4; 1, 3, 3, 3, 5; 1, 2, 3, 3, 2, 6; 1, 4, 3, 4, 3, 4, 7; 1, 2, 4, 4, 4, 4, 2, 8; 1, 5, 3, 3, 5, 3, 3, 5, 9; 1, 2, 4, 4, 5, 5, 4, 4, 2, 10; ... MAPLE g:= proc(n, k) local x, S; S:= {k}; x:= k; do x:= iquo(n, x) + irem(n, x); if member(x, S) then return x fi; S:= S union {x}; od end proc: for n from 1 to 20 do seq(g(n, k), k=1..n) od; MATHEMATICA T[n_, k_] := Module[{x, S}, S = {k}; x = k; While[True, x = Quotient[n, x] + Mod[n, x]; If[MemberQ[S, x], Return[x]]; S = S~Union~{x}]]; Table[T[n, k], {n, 1, 20}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 16 2022, after Robert Israel *) PROG (Python) def T(n, k): seen, x = set(), k while x not in seen: seen.add(x); q, r = divmod(n, x); x = q + r return x print([T(n, k) for n in range(1, 14) for k in range(1, n+1)]) # Michael S. Branicky, Oct 04 2022 CROSSREFS Cf. A357610. Sequence in context: A334230 A275723 A198338 * A199086 A098053 A272907 Adjacent sequences: A357551 A357552 A357553 * A357555 A357556 A357557 KEYWORD nonn,tabl,look AUTHOR J. M. Bergot and Robert Israel, Oct 02 2022 STATUS approved

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Last modified September 18 14:47 EDT 2024. Contains 376000 sequences. (Running on oeis4.)