A075257 Smaller terms in the pairs of numbers (a < b) in the sequence {a,b}-> {Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]} with k=3 and the first pair {a=1,b=2}. See A075256.

1, 1, 2, 1, 3, 2, 6, 1, 3, 9, 5, 15, 7, 21, 17, 46, 5, 15, 45, 73, 62, 157, 29, 87, 261, 94, 282, 407, 439, 782, 535, 1605, 206, 618, 1854, 2137, 3425, 2986, 7289, 1669, 5007, 15021, 170, 510, 1530, 4590, 13770, 24493, 16817, 50451, 6211, 18633, 55899

Offset

1,3

Comments

Take any pair {a,b}. Each next pair is get by the rule {a,b} -> Sort[{Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]]. Here k=3 and the first {a,b}={1,2}. For k = 2 there is a fixed point {a,b=2a}. For k > 2, are there any limits or cycles of the sequence {for some initial pair {a,b}?

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..1000

Formula

a(n) = A075256(2*n-1).

Mathematica

ss=Table[0, {j, 100}]; s=ss[[1]]={1, 2}; Do[ss[[i]]=Sort[{Max[s]-Min[s], 3*Min[s]}]; s=ss[[i]], {i, 2, 100}]; Table[Flatten[ss][[i]], {i, 1, 199, 2}]

Prog

(PARI) my(x=1, y=2); print1(x, ", "); for(n=2, 53, my(mx=max(x, y), mi=min(x, y)); x=min(mx-mi, 3*mi); y=max(mx-mi, 3*mi); print1(x, ", ")) \\ Hugo Pfoertner, Mar 21 2020

Crossrefs

Cf. A075256, A075258.

Sequence in context: A266138 A014000 A339612 * A260618 A306286 A226651

Adjacent sequences: A075254 A075255 A075256 * A075258 A075259 A075260

Keyword

nonn

Author

Zak Seidov, Sep 10 2002

Status

approved