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Numbers of the form k^2 -1 such that every partial product is also of the form k^2-1.
3

%I #8 Dec 05 2013 19:56:50

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

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

%C 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

%F a(n+1) = A084702(A093959(n)-1). - _David Wasserman_, May 03 2007

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

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

%Y Cf. A084702, A093959.

%K hard,nonn

%O 1,1

%A _Amarnath Murthy_, May 22 2004

%E More terms from _David Wasserman_, May 03 2007