A130532 a(n) + a(n - 1) is alternatively a square or a cube, a(1) = 1.

1, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 1, 7, 2, 6, 3, 5, 4, 4

Offset

1,2

Comments

a(1) = 1; a(2n) is a minimal positive m such that a(2n - 1) + m is a square, a(2n + 1) is a minimal positive m such that a(2n) + m is a cube. Sequence is periodic (apparently with the same period for any a(1)).

Links

Table of n, a(n) for n=1..105.

Example

a(1)=1, a(2)=3 because 1+3 is a square, a(3)=5 because 3+5 is a cube, a(4)=4 because 5+4 is a square, etc.

Mathematica

b=1; s={b}; Do[Do[bi=b+i; If[IntegerQ[Sqrt[bi]], b=i; AppendTo[s, b]; Break[]], {i, 1000}]; c=b; Do[ci=c+i; If[IntegerQ[ci^(1/3)], c=i; Break[]], {i, 1000}]; AppendTo[s, c]; b=c, {100}]; s

Crossrefs

Sequence in context: A195132 A086181 A000655 * A019707 A197825 A077861

Adjacent sequences: A130529 A130530 A130531 * A130533 A130534 A130535

Keyword

nonn

Author

Zak Seidov, Aug 08 2007

Status

approved