[seqfan] Re: A summer seq with second differences

Veikko Pohjola veikko at nordem.fi
Fri Aug 2 11:31:23 CEST 2013


Hi,
It appears that there is an infinite set of sequences having this property.
Veikko Pohjola


Aai kirjoitti 31.7.2013 kello 20.39:

> I didn't see a program to generate sequence A226930, so if of any use here's a generator in Haskell:
> 
> digits = map (fromIntegral.digitToInt). show
> inverseDiff xs = scanl (+) (head xs) xs
> seqA = iterate ((!!2). iterate inverseDiff. concatMap digits) [1]
> 
> Example (executed in GHCi):
> 
> ~> seqA !!4
> [1,2,4,8,16,32,49,72,98,126,158,199,247,297]
> 
> 
> 
> 
> 
> 
> On 31-07-13 14:49, Neil Sloane wrote:
>> Eric, nice sequence, as always! I added it as A226930.
>> I also added your comment to A164073.
>> Neil
>> 
>> 
>> On Tue, Jul 30, 2013 at 3:26 AM, Eric Angelini <Eric.Angelini at kntv.be>wrote:
>> 
>>> Many thanks, Paolo!
>>> And such sequences can be computed
>>> ad libitum for 3rd, 4th, 5th, ... nth differences, of course.
>>> 
>>> BTW could you add this comment
>>> to A164073 (as I have no access to it):
>>> "Absolute second differences are the
>>> sequence itself"
>>> (this might be suggested by the other
>>> comments but is not obvious to me).
>>> 
>>> Best,
>>> É.
>>> 
>>> Propulsé d'un aPhone
>>> 
>>> 
>>> 
>>> Le 30 juil. 2013 à 09:13, "Paolo Lava" <paoloplava at gmail.com> a écrit :
>>> 
>>>> It should start as:
>>>> 
>>>> 1, 2, 4, 8,16, 32, 49, 72, 98, 126, 158, 199, 247, 297, 356, 423, 491,
>>> 561,
>>>> 637, 714, 796, 886, 977, 1077, 1186, 1297, 1412, 1534, 1658, 1791, 1931,
>>>> 2074, 2222, 2376, 2534, 2694, 2857, 3024, 3200, 3377, 3559, 3747, 3936...
>>>> 
>>>> 
>>>> 2013/7/29 Eric Angelini <Eric.Angelini at kntv.be>
>>>> 
>>>>> Hello SeqFans,
>>>>> 
>>>>> S=1,2,4,8,16,32,49,72,98,126,158,199,247,297,352,423,...
>>>>> Compute the second differences and... look who's coming back!
>>>>> 
>>>>> Best,
>>>>> É.
>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>>> _______________________________________________
>>>>> 
>>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>>> 
>>>> _______________________________________________
>>>> 
>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>> _______________________________________________
>>> 
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>> 
>> 
>> 
> 
> -- 
> Met vriendelijke groet,
> @@i = Arie Groeneveld
> 
> 
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> 
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> 




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