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

1,1

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-François 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: A353308 A304807 A045920 * A071344 A224855 A366938

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