# [seqfan] Re: New Prime Curio about 9298 by Post

Jonathan Post jvospost3 at gmail.com
Thu Sep 10 04:05:04 CEST 2009

```Furthermore, if we take digital sums, some of this sequence about
primes and squares are connected in a second way to primes {20, 203,
1202, 2810, 2867, 3983, 4645, 5602, 18482,  19858, 35605, 40405, ...}
or squares {10, 178, 1618, 4939, 9691, 13138, 21445, 43243, ...}.
Is either such "base" subsequence worth submitting to OEIS?:

A038693 formatted as a simple table:
n		a(n)     SOD(a(n)) = A007953(a(n))
1		10       1+0 = 1 = 1^2
2		20       2+0 = 2 is prime
3		183     1+8+3 = 12
4		145     1+4+5 = 10
5		178     1+7+8 = 16 = 2^4
6		203     2+0+3 = 5 is prime
7		802     8+0+2 = 10
8		1131   1+1+3+1 = 6
9		1202   1+2+0+2 = 5 is prime
10		1618   1+6+1+8 = 16 = 2^4
11		2810   2+8+1+0 = 11 is prime
12		2867   2+8+6+7 = 23 is prime
13		3218   3+2+1+8 = 14
14		3983   3+9+8+3 = 23 is prime
15		4645   4+6+4+5 = 19 is prime
16		4939   4+9+3+9 = 25 = 5^2
17		5602   5+6+0+2 = 13 is prime
18		6989   6+9+8+9 = 32 = 2^5
19		9023   9+0+2+3 = 14
20		9298   9+2+9+8 = 28
21		9407   9+4+0+7 = 20
22		9691   9+6+9+1 = 25 = 5^2
23		10562  1+0+5+6+2 = 14
24		12205  1+2+2+0+5 = 10
25		13138  1+3+1+3+8 = 16 = 2^4
26		14907  1+4+9+0+7 = 21
27		16739  1+6+7+3+9 = 26
28		16805  1+6+8+0+5 = 20
29		18482  1+8+4+8+2 = 23 is prime
30		19443  1+9+4+4+3 = 21
31		19858  1+9+8+5+8 = 31 is prime
32		21445  2+1+4+4+5 = 16 = 2^4
33		26941  2+6+9+4+1 = 22
34		28803  2+8+8+0+3 = 21
35		35605  3+5+6+0+5 = 19 is prime
36		35689  3+5+6+8+9 = 31 is prime
37		40405  4+0+4+0+5 = 13 is prime
38		43243  4+3+2+4+3 = 16 = 2^4

On Wed, Sep 9, 2009 at 1:14 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> I'm sure if this list is complete, for4-digit integers for which has
> the property that the concatenation of prime factors is a square.
>
> 1131, 1202, 1618, 2810, 2867, 3218, 3983, 4645, 4939, 5602, 6989,
> 9023, 9298, 9407, 9691
>
> A038693   Numbers n such that concatenation of prime factors is a
> perfect square.
>
> Hence, although I may have submitted one or more of these before, I've
> as often as possible tried to give an additional property, which makes
> the number the smallest with both property (i.e. is an emirpimes, is
> the reveral of a prime).
>
> Has the Sarah Palinprime panel removed some such too hastily, missing
> the point of my ANDing of properties to make the submission smallest
> possible?
>
> 1131 and its reverse both have 3 distinct prime factors (2810 is 2nd smallest)
> 1202 is emirpimes ( 3983 is 2nd smallest, 3rd is 9691)
> 1618 semiprime whose reversal is prime (2nd smallest is 3218, 3rd is 9023)
> 2810 see 1131 above
> 3218 see 1618 above
> 3983 see 1202 above
> 4939 1st two digits make a square
> 9023 see 1618 above
> 9298 as just submitted, where curiously 9298 = 63^2 + 73^2 and 6373 is prime
> 9407, whose reversal ends in a 2-digit prime
> 9691 see 1202 above
>
> I may have mentioned other properties in prior such submissions.
>
> 10562 is the smallest such 5-digit number...
>
> Best,
>
> Jonathan Vos Post
>
>
>
> On Wed, Sep 9, 2009 at 12:12 PM, G. L. Honaker Jr<honak3r at gmail.com> wrote:
>> Is this the smallest case?
>>
>> G. L.
>>
>>
>>
>> On Wed, Sep 9, 2009 at 2:52 PM, Prime Curios! automailer for
>> <jvospost3 at gmail.com> wrote:
>>>
>>> There has been a new curio submitted for your approval:
>>>
>>> 9298 [number_id=9456]
>>>
>>> 9298 = 2 * 4649: concatenate its prime factors for the
>>> square of a prime, 24649 = 157^2. Its reversal 8929 is
>>> prime. [Post]
>>>
>>>
>>> You may see, make visible, edit... this entry at
>>>
>>>        http://primes.utm.edu/curios/page.php?number_id=9456&edit=1
>>>
>>> Technical info about the submitter:
>>> Connected from: 71.94.157.144
>>> via:
>>> accepts languages:
>>>
>>
>>
>

```