[seqfan] Re: A090566.

[Emmanuel Vantieghem]

That variant would be the sequence
1, 6, 4, 9, 61, 504, 1, 21, 16, 9, 216, 225, 625, 681, 21, 316, 84, \
1, 44, 1, 96, 100, 489, 2944, 656, 1, 156, 25, 6, 25, 281, 961, 6201, \
5625, 43524, 36729, 7225, 344, 569, 2996, 361, 201, 64, 516, 961, \
18416, 11396, 70081, 9729, 8496, 64201, 4244, 5225, 796, 3684, 49, \
284, 2596, 9216, 68881, 70025, 332129, 758249, 100625, 356225, \
147716, 466921, 2218896, 243216, 6489, 9136, 11076, 24961, 156081, \
885184, 4792025, 8622916, 4553156, 3253264, 99876, 225024, 999424, \
1308689, 2291561, 7924676, 1264225, 886884, 13636, 77184, 508041, \
2316529, 660225, 3165225, 275664, 901444, 1788836, 700676, 78209, \
7156, 16001
The square roots of the concatenations being
4, 8, 7, 31, 248, 71, 11, 46, 13, 96, 465, 475, 791, 261, 146, 178, \
29, 12, 21, 14, 310, 317, 2212, 1716, 81, 34, 125, 16, 25, 159, 531, \
3101, 7875, 23718, 65973, 19165, 2688, 587, 2386, 1731, 601, 142, \
254, 719, 9804, 42914, 33759, 26473, 9864, 29149, 25338, 6515, 2286, \
2822, 607, 222, 1686, 5096, 30359, 82995, 264623, 576307, 870775, \
317215, 596846, 384339, 2160836, 1489596, 49317, 8056, 30226, 33281, \
157991, 395072, 2975205, 6922446, 9285966, 6747708, 570374, 316032, \
474368, 3161367, 3617581, 4787026, 8902065, 1124378, 297806, 36928, \
277821, 2253977, 1522015, 2569485, 1779108, 525038, 3002406, 1337474, \
264703, 27966, 26751

The program for A264770 has to be slightly modified as follows :
A = {1, 6}; i = 2; M = {4}; While[i < 100, i++; m = Last[A]; d = 0;
 flag = 0;
 While[flag == 0, d++; g0 = Ceiling[Sqrt[m 10^d + 10^(d - 1)]];
  h = (m + 1) 10^d; a = g0; Label[L$];
  If[a^2 < h, b = a^2 - m 10^d;
   If[MemberQ[M, a], a++; Goto[L$], flag = 1; AppendTo[A, b];
    AppendTo[M, a]]]]];A

Emmanuel.

2015-11-25 0:50 GMT+01:00 David Wilson <davidwwilson at comcast.net>:

> Another variant:
>
> a(n) = smallest values such that the square number concat(a(n-1), a(n))
> has not yet been seen.
>
> > -----Original Message-----
> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> > Sloane
> > Sent: Tuesday, November 24, 2015 12:24 AM
> > To: Sequence Fanatics Discussion list
> > Subject: [seqfan] Re: A090566.
> >
> > David or Bob, What about this version of the sequence?
> > a(1) = 1, a(n) = smallest number NOT YET IN THE SEQUENCE such that the
> > concatenation of a(n-1) and a(n) is a square.
> >
> > It starts rather like A082209, 1, 6, 4, 9, 61, 504, 100, ... but it
> isn't in the OEIS.
> > Oh, maybe it dies - could you check?
> >
> > Neil
> > >
>
>
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