New sequence??

[Don Reble]

> ...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