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A242466 A term in this sequence a(n) is such that n and n+1 have isomorphic factor decomposition binary trees. 1
2, 9, 14, 21, 25, 33, 34, 38, 57, 85, 86, 93, 94, 116, 118, 121, 122, 133, 141, 142, 145, 158, 170, 171, 177, 201, 202, 205, 213, 214, 217, 218, 253, 284, 298, 301, 302, 326, 332, 334, 361, 369, 381, 387, 393, 394, 434, 435, 445, 446, 453, 481, 501, 514, 526 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Integral Fission (consecutive isomorphic trees): For a natural number, n, make it the root node of a binary tree. The left child node (L) is the largest divisor of n which is greater than 1 but less than or equal to the square root of n, if this exists. The right child node is n/L, if the left node exists. Thus if n is a prime it is a leaf node; otherwise if it is composite then it is the product of its two children. If n = 1 then we have an empty tree.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Gordon Hamilton, Integral Fission, Video for grade 7 teachers

MAPLE

with(numtheory):

t:= proc(n) option remember; `if`(n=1, "0",

      `if`(isprime(n), "10", (d-> cat("1", t(d), t(n/d), "0"))(

       max(select(x-> is(x<=sqrt(n)), divisors(n))[]))))

    end:

a:= proc(n) option remember; local k;

      for k from 1 +`if`(n=1, 0, a(n-1))

      while t(k)<>t(k+1) do od; k

    end:

seq(a(n), n=1..60);  # Alois P. Heinz, Aug 09 2014

MATHEMATICA

t[n_] := t[n] = If[n == 1, "0", If[PrimeQ[n], "10", ("1" <> t[#] <> t[n/#] <> "0"&)[Max[Select[Divisors[n], # <= Sqrt[n]&]]]]];

a[n_] := a[n] = (For[k = 1 + If[n == 1, 0, a[n-1]], t[k] != t[k+1], k++]; k);

Array[a, 60] (* Jean-Fran├žois Alcover, Mar 27 2017, after Alois P. Heinz *)

PROG

(PARI) isok(n) = eqvec(empty(fiss(n)), empty(fiss(n+1))); \\ using A125508 scripts; Michel Marcus, May 25 2014

CROSSREFS

Cf. A125508.

Sequence in context: A288483 A304807 A045920 * A071344 A224855 A254608

Adjacent sequences:  A242463 A242464 A242465 * A242467 A242468 A242469

KEYWORD

nonn

AUTHOR

Gordon Hamilton, May 15 2014

EXTENSIONS

More terms from Michel Marcus, May 25 2014

STATUS

approved

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Last modified June 12 19:31 EDT 2021. Contains 344960 sequences. (Running on oeis4.)