reviewed

approved

proposed

reviewed

editing

proposed

Comment from _Eric Angelini_, Aug 19 2008: The rule "monotonically increasing sequence where the size of each run of consecutive integers is given by the sequence itself" produces this sequence without the initial 0. - _Eric Angelini_, Aug 19 2008

A. S. Fraenkel, <a href="http://www.integers-ejcntemis.orgde/journals/INTEGERS/papers/eg6/eg6.Abstract.html">New games related to old and new sequences</a>, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

approved

editing

Comment from _Eric Angelini (eric.angelini(AT)skynet.be), _, Aug 19 2008: The rule "monotonically increasing sequence where the size of each run of consecutive integers is given by the sequence itself" produces this sequence without the initial 0.

_N. J. A. Sloane (njas(AT)research.att.com), _, Apr 02 2003

nonn,new

nonn

N. J. A. Sloane (njas, (AT)research.att.com), Apr 02 2003

Comment from Eric Angelini (eric.angelini(AT)skynet.be), Aug 19 2008: The rule "monotonically increasing sequence where the size of each run of consecutive integers is given by the sequence itself" produces this sequence without the initial 0.

nonn,new

nonn

A. S. Fraenkel, New games related to old and new sequences, preprint, 2003.

A. S. Fraenkel, <a href="http://www.integers-ejcnt.org/">New games related to old and new sequences</a>, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

Let a(n) = this sequence, b(n) = A081689. Then a(n) = mex{ a(i), b(i) : 0 <= i < n}, b(n) = b(n-1) + a(n) + 1. Apart from initial zero, complement of A081689.

nonn,new

nonn

0 followed by A030124 - 1.

0, 1, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77

0,3

From P-positions in a certain game.

A. S. Fraenkel, New games related to old and new sequences, preprint, 2003.

A. S. Fraenkel, <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/">Home Page</a>

Let a(n) = this sequence, b(n) = A081689. Then a(n) = mex{ a(i), b(i) : 0 <= i < n}, b(n) = b(n-1) + a(n) + 1.

Cf. A030124, A005228, A081689.

nonn

njas, Apr 02 2003

approved