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 A252230 Triangular array T read by rows:  for j = k+1..2*k, k >=1, T(j,k) = least number of iterations of (h,i) -> (i,h-i) needed to take (k,j) to (k',j') satisfying k' <= j'. 1
 1, 2, 1, 2, 3, 1, 2, 2, 3, 1, 2, 2, 4, 3, 1, 2, 2, 2, 3, 3, 1, 2, 2, 2, 4, 3, 3, 1, 2, 2, 2, 2, 5, 3, 3, 1, 2, 2, 2, 2, 4, 3, 3, 3, 1, 2, 2, 2, 2, 2, 4, 3, 3, 3, 1, 2, 2, 2, 2, 2, 4, 5, 3, 3, 3, 1, 2, 2, 2, 2, 2, 2, 4, 3, 3, 3, 3, 1, 2, 2, 2, 2, 2, 2, 4, 6 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Max(row n) = A088858(n).  Let F = A000045 (Fibonacci numbers).  Then T(j,k) is the least h such that one of the following holds:  h is odd and F(h+2)/F(h+1) <= j/k, or h is even and F(h+2)/F(h+1) >= j/k. LINKS Clark Kimberling, Rows n = 1..100, flattened EXAMPLE First 11 rows: 1 2 1 2 3 1 2 2 3 1 2 2 4 3 1 2 2 2 3 3 1 2 2 2 4 3 3 1 2 2 2 2 5 3 3 1 2 2 2 2 4 3 3 3 1 2 2 2 2 2 4 3 3 3 1 2 2 2 2 2 2 4 3 3 3 3 1 Note, for example, that the numbers in row 8 are T(8,9) to T(8,16); e.g., T(8,13) counts these 5 iterations:  (13,8) -> (8,5) -> (5,3) -> (3,2) -> (2,1) -> (1,1). MATHEMATICA f[n_] := Fibonacci[n]; h[j_, k_] := Select[Range[40], (OddQ[#] && f[# + 2]/f[# + 1]<= j/k) || (EvenQ[#] && f[# + 2]/f[# + 1] >= j/k) &, 1]; t[k_] := Flatten[Table[h[j, k], {j, k + 1, 2*k}]]; TableForm[Table[t[k], {k, 1, 26}]] ; (* A252230 array *) Flatten[Table[h[j, k], {k, 1, 100}, {j, k + 1, 2*k}]] (* A252230 sequence *) CROSSREFS Cf. A000045, A088858 Sequence in context: A183198 A249160 A269970 * A036043 A238966 A128628 Adjacent sequences:  A252227 A252228 A252229 * A252231 A252232 A252233 KEYWORD nonn,easy,tabl AUTHOR Clark Kimberling, Jan 09 2015 STATUS approved

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