[seqfan] Re: A090566.

[israel at math.ubc.ca]

Presumably you want a(n) >= 1, even if concatenation of a(n-1) and 0 is a 
square (since we don't want leading zeros in the next one).

1, 6, 4, 9, 61, 504, 100, 489, 2944, 656, 3844, 34449, 85636, 516, 961, 
6201, 5625, 43524, 36729, 7225, 344, 569, 2996, 361, 201, 64, 1601, 6004, 
7001, 316, 84, 681, 21, 16, 81, 225, 625, 5001, 3184, 3449, 2129, 8225, 
424, 36, 481, 636, 804, 609, 1024, 144, 400, 689, 5876, 7556, 8249, 53284, 
16016, 80441, 16721, 55664, 380489, 118244, 513689, 5326784, 14349929, 
2016161, 447056, 716129, 71236, 97604, 52025, 92641, 705641, 3144881, 
1589776, 384, 1600, 8001, 3025, 16449, 51364, 45561, 15001, 3504, 6400, 
900, 601, 2304, 324, 3601, 2001, 6676, 5241, 76, 176, 89, 401, 956, 484, 
416, ...

It can't die: for any x >= 1, if d is sufficiently large there are more 
than n squares between 10^d*x + 10^(d-1) and 10^d*x + 10^d - 1.

I'll contribute it.

Cheers,
Robert

On Nov 23 2015, Neil Sloane wrote:

>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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