[seqfan] Re: Happy 3³+4³+5³+6³+7³+8³+9³

[Veikko Pohjola]

Jean-Paul,

Merci pour ta spécification en ce qui concerne les coutumes francaises associés à Nouvelle Année. Ma connaissance est basée seulement sur ce que nous ont raconté nos amis français. Je viens de recevoir des souhaits de l’année 2016 avant-hier, et l’année dernière c’ètait aussi, selon le coutume, à la fin de janvier. Heureusement il semble qu’il y en a plus qu’un seul stéréotype national. 

Cordialement,
Veikko


jean-paul allouche kirjoitti 30.1.2016 kello 23.26:

> Dear all
> 
> May I suggest that it is not quite true that French people wait till the end of January
> to send New Year's greetings! They usually do so at the very beginning of January,
> but they find quite ok if they send or receive greetings before the 10th for elderly
> people. Younger people might find ok to wait till the 15th; more rarely till the 25th
> (or even a bit later) but it is then considered as not really ok by less young people...
> 
> best wishes
> jp
> 
> 
> Le 30/01/16 19:19, Veikko Pohjola a écrit :
>> Dear Giovanni and others,
>> 
>> The French have a custom to send New Year's greetings at the end of January. So I got the idea to play a little with the charming geometrical problem, number 7 below. The side lengths of the triangles, where all the sides are integral and satisfy the condition of green squares x+y=z, form each a nice sequence as the triangle grows. The smallest side goes like this: 13,17,25,37,41,53,61, …
>> 
>> Happy New Year,
>> Veikko Pohjola
>> 
>> Giovanni Resta kirjoitti 4.1.2016 kello 10.59:
>> 
>>> Other notable properties of 2016:
>>> 
>>> (1) The middle value y of the smallest amicable triple, i.e., 3 numbers x < y < z such that sigma(x)=sigma(y)=sigma(z) = x+y+z \sigma(n) is the sum of the divisors of n.
>>> 
>>> (2) The only number n such that n^3 + n^2 is strictly pandigital, i.e., it contains all the digits 0 to 9 exactly once.
>>> 
>>> (3) The smallest number equal to the sum of its 31 smallest divisors.
>>> 
>>> (4) The smallest number whose square root begins with 10 composite digits (so 4, 6, 8 or 9).
>>> 
>>> (5) If p(n) denotes the n-th prime number, the product of digits of p(p(666)) is 2016.
>>> 
>>> (6) T(rev(iT(2016))) = 666, where T(n) is the n-th triangular number, rev(n) is the reverse of n, and iT(T(n))=n.
>>> 
>>> (7) The value of y in this geometrical problem http://www.numbersaplenty.com/prob2016.png
>>> 
>>> Giovanni Resta
>>> 
>>> 
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