[seqfan] Re: Middle digit in square numbers

[Olivier Gerard]

There is an interesting phenomena going on with
a related sequence

numbers whose square has an even number of digits
in base 10 and the two middle digits are equal.

83^2 = 6889 is in this sequence.

35, 38, 46, 65, 76, 83, 85, 318, 335, 348, 359, 380, 383, 393, 400,
415, 419, 432, 436, 441, 457, 469, 500, 511, 526, 527, 585, 586, 599,
600, 611, 620, 636, 648, 654, 665, 688, 692, 696, 700, 711, 718, 728, ...
(not yet in the OEIS, will be A279410)

For certain modulo (such as 43, 61, 75) the residues display nice
patterns close to concentric hyperboles (compute it at least up to 5000
to see them correctly).


Olivier


On Mon, 12 Dec 2016 at 11:30 Jeremy Gardiner <jeremy.gardiner at btinternet.com>
wrote:

>
> Consider also cubes:
>
> 0: 0, 30, 40, 42, 100, 101, 115, 116, 123, 126, 135, 163, 164, 171, 199,
> 1: 1, 6, 8, 23, 44, 45, 102, 106, 110, 114, 117, 121, 137, 148, 152, 153,
> 2: 5, 9, 103, 113, 133, 146, 151, 154, 165, 180, 198,
> 3: 29, 34, 39, 46, 118, 125, 141, 142, 155, 161, 170,
> 4: 7, 104, 112, 140, 143, 158, 166, 186, 188, 195,
> 5: 26, 43, 107, 109, 119, 122, 136, 139, 144, 150, 177, 179, 197,
> 6: 22, 25, 27, 36, 37, 124, 129, 134, 147, 156, 160, 169,
> 7: 31, 32, 105, 111, 128, 130, 149, 167, 173, 191, 192,
> 8: 2, 24, 35, 38, 120, 127, 131, 138, 145, 172, 174, 182, 183,
> 9: 28, 33, 41, 108, 132, 157, 159, 175, 178, 181, 184, 187, 190, 193, 196,
>
>