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A309228 a(n) is the greatest possible height of a binary tree where all nodes hold positive squares and all interior nodes also equal the sum of their two children and the root node has value n^2. 1
1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 3, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 3, 3, 1, 2, 1, 1, 3, 1, 2, 3, 1, 1, 1, 4, 1, 1, 3, 1, 2, 1, 1, 3, 3, 3, 1, 1, 3, 1, 2, 1, 3, 1, 1, 4, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The sequence is unbounded and for any k > 0, A309167(k) is the least n such that a(n) = k.

LINKS

Table of n, a(n) for n=1..87.

FORMULA

a(n) = 1 iff n belongs to A004144.

a(A309167(n)) = n.

If n^2 = u^2 + v^2 with u > v > 0, then a(n) >= 1 + max(a(u), a(v)).

EXAMPLE

a(1) = 1:

              1^2

               |

a(5) = 2:

           3^2    4^2

            \     /

             \   /

              5^2

               |

a(13) = 3:

          3^2    4^2

           \     /

            \   /

             5^2    12^2

              \      /

               \    /

                13^2

                  |

PROG

(PARI) a = vector(87, n, 1); for (n=1, #a, for (u=1, n-1, if (issquare(v2=n^2-u^2), a[n]=max(a[n], 1+max(a[u], a[sqrtint(v2)])))); print1 (a[n]", "))

CROSSREFS

Cf. A004144, A309167.

Sequence in context: A084115 A284154 A080028 * A309778 A143223 A063993

Adjacent sequences:  A309225 A309226 A309227 * A309229 A309230 A309231

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jul 16 2019

STATUS

approved

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Last modified January 20 08:18 EST 2020. Contains 331081 sequences. (Running on oeis4.)