A125508 -id:A125508 - cp's OEIS frontend

A242466 A term in this sequence a(n) is such that n and n+1 have isomorphic factor decomposition binary trees.

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

Offset: 1

Gordon Hamilton, May 15 2014

nonn

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.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Gordon Hamilton, Integral Fission, Video for grade 7 teachers

Cf. A125508.

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

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-François Alcover, Mar 27 2017, after Alois P. Heinz *)

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

More terms from Michel Marcus, May 25 2014

cp's OEIS Frontend

A242466 A term in this sequence a(n) is such that n and n+1 have isomorphic factor decomposition binary trees.

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