185 is special

[Jon Schoenfield]

Tanya,

How about "20-gonal numbers that can be expressed as the sum of two squares 
in more than one way"?  I get

185, 820, 1417, 2465, 5876, 10132, 12025, 17865, 22100, 29812, 33001, 37505, 
56960, 59860, 64345, 70577, 72180, 83905, 91001, 96512, 114017, 132980, 
139625, 167825, 188065, 190676, 209457, 220585, 234900, 255697, 258740, 
267977, 283732, 293401, 306545, 347705, 365620, 387712, 425972, 453825, 
457876, 470137, 482560, 486737, 490932, 520801, 538265, 592385, 611001, 
629905, 663680, 673492, 708401, ...

(I got the idea from  http://en.wikipedia.org/wiki/185_%28number%29  )

The only other sequence possibly beginning with 185 that I've thought of 
would be of no general interest -- my weight in pounds at my n-th wedding 
anniversary.  (Not monotonically increasing, but definitely an overall 
upward trend over the 20-something terms thus far ....)   :-/

<<  The next one is 214 followed by 230.  >>

Wikipedia offers the following:

214:

Two hundred fourteen 214 = 2·107, Mertens function returns 0, nontotient, 
form DD 214 documents discharge from the U.S. Armed Forces, SMTP status code 
for help message, title of one of the first hit songs of the popular 
Filipino band Rivermaya (released in 1994), which reached the Number One 
spot shortly after its release

230:

It is a composite number, with its divisors being 2, 5, 10, 23, 46, and 115. 
Its factorisation makes it a sphenic number. There is no integer with 230 
coprimes below it, thus 230 is a nontotient. However, the sum of the coprime 
counts for the first 27 integers is 230.
There are 230 unique space groups describing all possible crystal 
symmetries.
In base 10, being divisible by the sum of its digits, 230 is a Harshad 
number.

I looked a while back (sometime last year?) for the smallest positive number 
not listed among the terms of any sequence in the OEIS, and I think it was 
somewhere in the upper 9000s.  I don't know if it's still in that range....

-- Jon

----- Original Message ----- 
From: "Tanya Khovanova" <tanyakh at TanyaKhovanova.com>
To: "sequence fans" <seqfan at ext.jussieu.fr>
Sent: Thursday, May 31, 2007 8:40 PM
Subject: 185 is special


> Hello seqfans,
>
> 185 is the smallest positive number that doesn't start any sequence. Do 
> you know anything special about 185 that might start a sequence?
>
> The next one is 214 followed by 230.
>
> Tanya
>
>
> _________________________________________________________________
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* zak seidov <zakseidov at yahoo.com> [Jun 01. 2007 11:08]:
> Dear seqfans, 
> Please anybody explain me (and Neil) 
> what's wrong with this SEQ?
> My explanations were simply ignored by Neil.
> Thanks, Zak
> 

This is a prime example of a sequence that shouldn't
ever be entered into the OEIS.  A sequence for its
own sake, no relation to nothing, made up, never of
use for anybody, likely to generate false hits.


> 
> [...]
> %N A129755 Triangular numbers t such that t+10 is a prime.

There are plenty of interesting sequences that are worth
being entered into the OEIS.  This is not one of them.


> %K A129755 nonn,new,uned,obsc,less

... for the lack of the keyword "spam"


> %O A129755 1,2
> %A A129755 Zak Seidov (zakseidov(AT)yahoo.com), May 15
> 2007
> %E A129755 I received several confusing emails about
> this sequence. It should be rechecked. - njas, May 29
> 2007

What about giving _code_, is it so much work to type

? for(k=1,100,t=(k*(k+1))/2,if(isprime(t+10),print1(k,", ")))

into pari/gp?


> [...]


I continue to marvel at Neil's patience.