OFFSET
1,1
COMMENTS
This sequence does not include every natural number. Suppose it contains b^2. Then letting A be the product up to b^2, we have A + 1 = i^2 and b^2 A + 1 = j^2. Multiplying the first equation by b^2 and subtracting, we get (bi)^2 = j^2 + b^2 - 1, which puts an upper bound on i and j (and hence on A). Probably the sequence contains no squares other than 1. - Franklin T. Adams-Watters, Aug 29 2006
a(n) <= 2 + Product_{k=1..n-1} a(k). - Max Alekseyev, Apr 26 2010
EXAMPLE
3 + 1 = 4, 3*1*5 + 1 = 16, 3*1*5*8 + 1 = 121 etc. are squares.
PROG
(PARI) v=[1]; n=1; while(n<1100, s=1+n*prod(i=1, #v, v[i]); if(issquare(s)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v \\ Derek Orr, Jun 16 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, May 22 2004
EXTENSIONS
More terms from Franklin T. Adams-Watters, Aug 29 2006
a(11) from D. S. McNeil, Mar 20 2009
a(12) from Sean A. Irvine, Nov 18 2009
a(13)-a(15) from Max Alekseyev, Apr 26 2010
STATUS
approved