A094357 Numbers of the form k^2 -1 such that every partial product is also of the form k^2-1.

3, 8, 15, 323, 115599, 13441619843, 180680260779332208399

Offset

1,1

Comments

Next term <= 32645356640144805339103579127542660095683 : The number (sqrt( product( a[j], j=1 .. n )+1)-1)^2-1 does satisfy the requirements for the next term, but is this always the smallest solution ? - M. F. Hasler, May 15 2007

Links

Table of n, a(n) for n=1..7.

Formula

a(n+1) = A084702(A093959(n)-1). - David Wasserman, May 03 2007

For n>1, a[n+1] <= floor( sqrt( product( a[j], j=1 .. n )))^2-1 - M. F. Hasler, May 15 2007

Example

3, 8 and 15 are 1 less than a square and so are the numbers 3, 3*8, 3*8*15.

Crossrefs

Cf. A084702, A093959.

Sequence in context: A120341 A325904 A362273 * A340003 A136532 A368041

Adjacent sequences: A094354 A094355 A094356 * A094358 A094359 A094360

Keyword

hard,nonn

Author

Amarnath Murthy, May 22 2004

Extensions

More terms from David Wasserman, May 03 2007

Status

approved