[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:
>>>
>>
>>
>
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