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

[jean-paul allouche]

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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