A268878 Breadth-first traversal of a binary tree in which the value at the n-th node is equal to ParentNode()*prime(n-1).

1, 2, 3, 10, 14, 33, 39, 170, 190, 322, 406, 1023, 1221, 1599, 1677, 7990, 9010, 11210, 11590, 21574, 22862, 29638, 32074, 84909, 91047, 118437, 123321, 164697, 171093, 182793, 189501, 1014730, 1046690, 1234370, 1252390, 1670290, 1692710, 1819630, 1889170

Offset

1,2

Comments

2 and 3 are the only primes in the sequence.

Each node N of the tree is divisible only by its ancestors.

All the nodes in a subtree T of T0 are divisible by T's root value.

Given two nodes in the tree, N and M, the common ancestor in the tree is GCD(N,M) (greatest common divisor of N and M).

Links

Davide Aversa, Table of n, a(n) for n = 1..1000

Formula

Recursive formula: a(1) = 1, a(n) = prime(n-1)* a(floor(n/2)).

The formula derives from the definition and the parent's index formula of a generic binary tree.

Example

For n=5, a(5) = prime(4)*a(floor(5/2)) = prime(4)*a(2) = prime(4)*prime(1)*a(floor(2/2)) = prime(4)*prime(1)*a(1) = 7*2*1 = 14.
The tree begins:
                   1
        2                    3
  10        14         33          39
170 190   322 406   1023 1221   1599 1677

Prog

(Python) # Recursive version
from sympy import prime
def a(n):
  if n < 3: return n
  return prime(n - 1) * a(n // 2)
print([a(n) for n in range(1, 19)])
(PARI) a(n) = if (n==1, 1, prime(n-1)* a(n\2)) \\ Michel Marcus, Feb 16 2016
(Magma) [n le 1 select 1 else NthPrime(n-1)* Self(Floor(n/2)): n in [1..60]]; // Vincenzo Librandi, Feb 17 2016

Crossrefs

Sequence in context: A129315 A171126 A299205 * A194544 A348475 A075770

Adjacent sequences: A268875 A268876 A268877 * A268879 A268880 A268881

Keyword

nonn,easy,tabf

Author

Davide Aversa, Feb 15 2016

Status

approved