[seqfan] Re: A summer seq with second differences

[Veikko Pohjola]

Bonjour Eric,
My comment relates to an earlier discussion concerning the problem of publishing (in OEIS) multiple sequences which are only instances of one sequence class. In this case: sequences which all have the property of having the sequence of its second differences being digitally identical to itself. Even, when the second difference is limited to be from 0 to 9, the number of such sequences is without limit.
Veikko

Eric Angelini kirjoitti 2.8.2013 kello 14.36:

> 
>> infinite
> 
> ... Indeed, Veikko, but the one in the OEIS is the lexicographically first one.
> 
> Propulsé d'un aPhone
> 
> 
> 
> Le 2 août 2013 à 11:31, "Veikko Pohjola" <veikko at nordem.fi> a écrit :
> 
>> 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.
>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>>> _______________________________________________
>>>>>>> 
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>>>>>>> 
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>>>> 
>>>> 
>>> 
>>> -- 
>>> Met vriendelijke groet,
>>> @@i = Arie Groeneveld
>>> 
>>> 
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>> 
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