A348067 -id:A348067 - cp's OEIS frontend

A076146 a(1) = 1; a(n) = a(n-1)*prime(a(n-1)).

1, 2, 6, 78, 30966, 11234495766, 3197149582479668022558

Offset: 1

Zak Seidov, Nov 02 2002

Previous term * prime(previous term). Previous term + prime(previous term) is A074271.

Matula-Goebel numbers of the finite ordinal numbers; see also A007097. - Gus Wiseman, Aug 30 2016

Cf. A033286, A074271, A007097, A000040, A004111, A348067.

NestList[# Prime@ # &, 1, 6] (* Michael De Vlieger, Aug 30 2016 *)

a(7) from Gus Wiseman, Aug 30 2016

A358650 Matula-Goebel tree number of the binomial tree of n vertices.

Original entry on oeis.org

1, 2, 4, 6, 12, 18, 42, 78, 156, 234, 546, 1014, 2886, 4758, 14118, 30966, 61932, 92898, 216762, 402558, 1145742, 1888926, 5604846, 12293502, 28210026, 45860646, 121727346, 249864654, 813198126, 1423166394, 4740553974, 11234495766, 22468991532, 33703487298

Offset: 1

Kevin Ryde, Nov 25 2022

The top-down definition of the binomial tree suits Matula-Goebel numbering: The tree of n = 2^k + r vertices, for 1 <= r <= 2^k is the binomial tree of 2^k vertices and a child subtree under the root which is the binomial tree of r vertices.

In the tree of n vertices, adding a new singleton child under each vertex gives the tree of 2*n vertices, so that a(2*n) = A348067(a(n)).

			The tree of n=13 vertices numbered 0..12 is
  0
  | \  \    \
  1  2  4     8
     |  | \   | \  \
     3  5  6  9 10  12
           |     |
           7    11
Vertices 0..7 are the binomial tree of 2^k = 8 vertices, and vertices 8..12 are the binomial tree of 5 vertices.
Using the recurrence, a(13) = a(8 + 5) = a(8) * prime(a(5)) = 78*37 = 2886.

Kevin Ryde, Table of n, a(n) for n = 1..117
Kevin Ryde, PARI/GP Code
Index entries for sequences related to Matula-Goebel numbers

Cf. A076146, A348067.

PARI
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a(2^k + r) = a(2^k) * prime(a(r)) for 1 <= r <= 2^k.

a(2^k) = A076146(k+1), being a tree of order k.

cp's OEIS Frontend

A076146 a(1) = 1; a(n) = a(n-1)*prime(a(n-1)).

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A358650 Matula-Goebel tree number of the binomial tree of n vertices.

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