A152721 A prime based vector recursion: a(n)={Prime[n+1],Prime[n],Prime[n-1],-Prime[n-2],...,-1,-1}.

-1, 1, -1, 5, -1, -1, 7, -5, -1, -1, 11, -7, -5, -1, -1, 13, -11, -7, -5, -1, -1, 17, -13, -11, -7, -5, -1, -1, 19, -17, -13, -11, -7, -5, -1, -1, 23, -19, -17, -13, -11, -7, -5, -1, -1, 29, -23, -19, -17, -13, -11, -7, -5, -1, -1, 31, -29, -23, -19, -17, -13, -11, -7, -5

Offset: 0

Author

Roger L. Bagula, Dec 11 2008

Keywords

• sign

Comments

Row sums are:

{-1, 0, 3, 0, -3, -12, -21, -36, -51, -68, -95,...}

Examples

			{-1},
{1, -1},
{5, -1, -1},
{7, -5, -1, -1},
{11, -7, -5, -1, -1},
{13, -11, -7, -5, -1, -1},
{17, -13, -11, -7, -5, -1, -1},
{19, -17, -13, -11, -7, -5, -1, -1},
{23, -19, -17, -13, -11, -7, -5, -1, -1},
{29, -23, -19, -17, -13, -11, -7, -5, -1, -1},
{31, -29, -23, -19, -17, -13, -11, -7, -5, -1, -1}
		

Crossrefs

A152568, A027293

Programs

Mathematica

b[0] = {-1}; b[1] = {1, -1};
b[n_] := b[n] = Join[{Prime[n + 1 ]}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];
Table[b[n], {n, 0, 10}]; Flatten[%]

Formula

a(n)={Prime[n+1],Prime[n],Prime[n-1],-Prime[n-2],...,-1,-1}.