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A094353
Smallest integer not yet used such that 1 + Product_{k=1..n} a(k) is a square.
3
3, 1, 5, 8, 7, 2, 17, 44, 53, 1011, 7262969, 27755899054, 10713771825916682198, 1451983503000530523834049701901973110, 5317619734003376302895262678416297955761358855419919105266696681033714
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
Cf. A094354.
Sequence in context: A280384 A124420 A176105 * A298662 A306780 A209996
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