New sequence??

[Richard Guy]

If  n = 26,  we want the least  t_n  so that some
subset of  26 + 1, 26 + 2, ..., 26 + t_n  has a
square product.  I make this to be

         27* 28 * 30 * 32 * 35

where  35 = 26 + 9,  giving  a(26) = 9.

a(0) = 1, because  0+1  is a square.
I don't understand the definition of the
sequence below of which you give 503 terms.   R.

On Thu, 1 Apr 2004, Don Reble wrote:

> > ...find the least value of $t_n$
> > so that the integers $n+1$, $n+2$, \ldots, $n+t_n$ contain a subset
> > the product of whose members with $n$ is a square.
> 
> > ... t_n  should appear in OEIS.  P'raps it does,
> > but you all know that I'm not a good looker.
> 
> > Not surprisingly it starts off like  A080883,
> > but  a(26) = 9,  I believe, because
> >     27 * 28 * 30 * 32 * 35 = 2520^2
> > ... probably lots of errors.
> 
> Indeed: that product shows that a(27)=8. Have I misunderstood something?
> Anyway, I get this sequence, starting from a(0):
> 
>          0   0   4   5   0  5   6   7   7   0
>          8  11   8  13   7  9   0  17   9  19
>         10   7  11  23   8  0  13   8  12  29
>         12  31  13  11  17 13   0  37  19  13
>         10  41  14  43  11 15  23  47   6   0
>         13  17  13  53  16 11  16  19  29  59
>         15  61  31  14   0 13  14  67  17  23
>         14  71  16  73  37 15  19  19  13  79
>         18   0  41  83  20 17  43  29  11  89
>         15  19  23  31  47 19  12  97  14  18
>          0 101  17 103  16 20  53 107  18 109
>         22  37  16 113  19 23  29  13  59  17
>         15   0  61  41  31 15  21 127  15  43
>         20 131  22  19  67 21  17 137  23 139
>         20  47  71  22   0 29  73  15  37 149
>         25 151  19  17  14 31  26 157  79  53
>         16  23  18 163  41 22  83 167  21   0
>         20  24  43 173  29 17  22  59  89 179
>         20 181  26  61  23 37  31  17  47  21
>         19 191  24 193  97 25   0 197  26 199
>         21  67 101  29  27 41 103  23  26  19
>         28 211  53  71 107 43  27  31 109  73
>         20  21  37 223  28  0 113 227  19 229
>         23  33  29 233  26 47  59  79  17 239
>          5 241   8  27  61 27  41  19  31  83
>         25 251  21  23 127 30   0 257  43  37
>         20  29 131 263  22 53  28  89  67 269
>         18 271  34  31 137 22  23 277 139  31
>         28 281  47 283  71 30  26  41  12   0
>         29  97  73 293  29 59  37  23 149  23
>         25  43 151 101  32 61  34 307  22 103
>         31 311  26 313 157 28  79 317  53  29
>         22 107  23  29   0 26 163 109  41  47
>         27 331  83  37 167 67  24 337  12 113
>         23  31  38  21  43 23 173 347  29 349
>         25  23  26 353  59 71  89  28 179 359
>         24   0 181  27  28 73  61 367  23  41
>         37  53  31 373  34 21  47  29  27 379
>         19 127 191 383  30 33 193  43  97 389
>         26  34  28 131 197 79  33 397 199  33
>          0 401  67  31 101 35  29  37  29 409
>         41 137 103  59  36 83  26 139  38 419
>         28 421 211  47  53 34  71  61 107  26
>         43 431  36 433  31 29 109  23  73 439
>         22   0  33 443  37 89 223 149  28 449
>         30  41 113 151 227 35  27 457 229  27
>         33 461  33 463  40 31 233 467  26  67
>         47 157  59  43  79 38  34  53 239 479
>         20  37 241  23   0 97  21 487  61 163
>         22 491  41  29  26 33  31  71  83 499
>         40 167 251
> 
> (Feel free to double-check, eh.) For many primes p, a(p)=p, so it's easy
> to find one's way through that list.
> 
> --
> Don Reble       djr at nk.ca
>