A242466 - OEIS

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

(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