[seqfan] Re: A summer seq with second differences

[Eric Angelini]

> 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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