A034797 a(0) = 0; a(n+1) = a(n) + 2^a(n).

0, 1, 3, 11, 2059

Offset

0,3

Comments

First impartial game with value n, using natural enumeration of impartial games.

The natural 1-1 correspondence between nonnegative numbers and hereditarily finite sets is given by f(A)=sum over members m of A of 2^f(m). A set can be considered an impartial game where the legal moves are the members. The value of an impartial game is always an ordinal (for finite games, an integer).

The next term, a(5) = 2^2059 + 2059, has 620 decimal digits and is too large to include. - Olivier Gérard, Jun 26 2001

Positions of records in A103318. - N. J. A. Sloane and David Applegate, Mar 21 2005

The first n terms in this sequence form the lexicographically earliest n-vertex clique in the Ackermann-Rado encoding of the Rado graph (an infinite graph in which vertex i is adjacent to vertex j, with i<j, when the i-th bit of the binary representation of j is nonzero). - David Eppstein, Aug 22 2014

This sequence was used by Spiro to bound the density of refactorable numbers (A033950). - David Eppstein, Aug 22 2014

References

J. H. Conway, On Numbers and Games, Academic Press.

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..5

Wilhelm Ackermann, Die Widerspruchsfreiheit der allgemeinen Mengenlehre, Math. Ann. 114 (1939), no. 1, 305-315.

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp. Preprint versions: [pdf, ps].

O. Kurganskyy and I. Potapov, Reachability problems for PAMs, arXiv preprint arXiv:1510.04121 [cs.NA], 2015.

Richard Rado, Universal graphs and universal functions, Acta Arith. 9 (1964), 331-340.

Claudia Spiro, How often is the number of divisors of n a divisor of n?, J. Number Theory 21 (1985), no. 1, 81-100.

Wikipedia, Rado graph.

Mathematica

a=0; lst={a}; Do[AppendTo[lst, a+=2^a], {n, 0, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, May 06 2010 *)
NestList[#+2^#&, 0, 5] (* Harvey P. Dale, Mar 22 2020 *)

Crossrefs

Cf. A034798, A103318.

Sequence in context: A124984 A287432 A353085 * A212814 A101710 A088799

Adjacent sequences: A034794 A034795 A034796 * A034798 A034799 A034800

Keyword

nonn

Author

Joseph Shipman (shipman(AT)savera.com)

Status

approved