New sequence??
Richard Guy
rkg at cpsc.ucalgary.ca
Fri Apr 2 18:03:35 CEST 2004
Sorry about that!! I wasn't including n.
Shift all my members one place. R.
On Thu, 1 Apr 2004, Richard Guy wrote:
> 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
> >
>
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