A064691 a(n) is the smallest number not already used such that a(n)*a(n-1)*a(n-2) + 1 is a square, with a(1)=1 and a(2)=2.

1, 2, 4, 3, 10, 12, 7, 20, 6, 8, 11, 5, 21, 16, 9, 35, 13, 72, 58, 65, 604, 1570, 483, 7868, 43510, 408, 1092, 659, 2030, 14316, 8639, 746852, 19897158, 2687632650, 2999086659168, 1284545911428706, 223248740282126298936, 327753663681964670057609684710, 356988962448345124133946312923274915552122, 585368332163743818626039069448750700022101290164211798116740578

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Example

a(3) = 4 because 1*2*4+1 = 9 = 3*3 a(4) = 3 because 2*4*3+1 = 25 = 5 * 5

Mathematica

a = {1, 2}; Do[ b = a[[ -2]]*a[[ -1]]; k = 3; While[ !IntegerQ[ Sqrt[k*b + 1]] || Position[a, k] != {}, k++ ]; Print[k]; a = Append[a, k], {n, 3, 33} ]; a

Crossrefs

Sequence in context: A240271 A208324 A277416 * A247071 A014664 A270600

Adjacent sequences: A064688 A064689 A064690 * A064692 A064693 A064694

Keyword

nonn,nice

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 11 2001

Extensions

More terms from Don Reble, Oct 13 2001

Status

approved