A081695 From P-positions in a certain game.

0, 1, 3, 7, 12, 13, 21, 30, 31, 42, 45, 60, 61, 78, 79, 98, 99, 121, 144, 145, 170, 171, 198, 199, 228, 231, 264, 265, 300, 301, 338, 339, 378, 379, 420, 422, 423, 469, 516, 517, 566, 567, 618, 619, 672, 673, 728, 729, 786, 787, 846, 849, 912, 913, 978, 979, 1046, 1047, 1116, 1117, 1188, 1189, 1262, 1263, 1338

Offset

0,3

Links

Table of n, a(n) for n=0..64.

A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

Formula

Let a(n) = A081694(n) and let b(n) = n-th term of the current sequence. Then a(n) = mex{ a(i), b(i) : 0 <= i < n}; b(n) = a(n) + b(n-1) - (1+(-1)^b(n-1))*a(n-1)/2. Also, apart from initial zero, current sequence is complement of A081694.

Maple

A081694 := proc(n)
    option remember;
    local i;
    if n <=1 then
        n;
    else
        { seq(procname(i), i=0..n-1)} union {seq(A081695(i), i=0..n-1)}  ;
        mex(%) ;
    end if;
end proc:
A081695 := proc(n)
    option remember;
    if n <= 1 then
        n;
    else
        A081694(n)+procname(n-1)-(1+(-1)^procname(n-1))*A081694(n-1)/2 ;
    end if;
end proc:
seq(A081695(n), n=0..70) ; # R. J. Mathar, Apr 13 2019

Crossrefs

Cf. A081694.

Sequence in context: A230109 A045134 A215631 * A290955 A270122 A142958

Adjacent sequences: A081692 A081693 A081694 * A081696 A081697 A081698

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 02 2003

Extensions

More terms from R. J. Mathar, Apr 13 2019

Status

approved