Farideh Firoozbakht wrote:
>...
>for n=0,...,100
>
> a(n)= :
> 1,1,2,4,1,2,4,9,2,4,9,30,15,4,9,30,97,84,84,26,15,127,
> 308,30,15,127,898,24,913,97,24,913,308,69,2,4,9,30,2996,
> 4217,308,560,97,69,1040,11,69,868,9,30,2996,7327,14566,
> 13618,39,11544,26,1938,913,2875,64695,4292,97,4288,1,2,4,9,
> 30,2996,64721,11852,13618,11852,84,30,2996,211582,13698,3909,
> 146861,26,1938,2972,4217,39494,433,676711,481203,146861,223434,
> 2972,2875,676711,11,69,146861,8,26,1938,7327
>
>and {n,a(n)}=:
>
> {0, 1},{1, 1},{2, 2},{3, 4},{4, 1},{5, 2},{6, 4},{7, 9},{8, 2},{9,4},
> {10, 9},{11, 30},{12, 15},{13, 4},{14, 9},{15, 30},{16, 97},{17, 84},
> {18, 84},{19, 26},{20, 15},{21, 127},{22, 308},{23, 30},{24, 15},
> {25, 127},{26, 898},{27, 24},{28, 913}, {29, 97},{30, 24},{31, 913},
> {32, 308},{33, 69},{34, 2},{35, 4},{36, 9},{37, 30},{38, 2996},
> {39, 4217},{40, 308},{41, 560},{42, 97},{43, 69},{44, 1040},{45, 11},
> {46, 69},{47, 868},{48, 9},{49, 30},{50, 2996},{51, 7327},{52, 14566},
> {53, 13618},{54, 39}, {55, 11544},{56, 26},{57, 1938},{58, 913},
> {59, 2875}, {60,64695},{61, 4292},{62, 97},{63, 4288},{64, 1},{65, 2},
> {66, 4},{67, 9},{68, 30},{69, 2996},{70, 64721}, {71, 11852},{72,13618}
> {73, 11852},{74, 84},{75, 30},{76, 2996},{77, 211582},{78, 13698},
> {79, 3909},{80, 146861},{81, 26},{82, 1938},{83, 2972}, {84, 4217},
> {85, 39494},{86, 433},{87, 676711},{88, 481203},{89, 146861},
> {90, 223434},{91, 2972},{92, 2875},{93, 676711}, {94, 11},{95, 69},
> {96, 146861},{97, 8},{98, 26},{99, 1938},{100, 7327}
>
>
>If the sequence has closed form, finding of it,is difficult.
>
>
>Regards,
>
>Farideh Firoozbakht
>UniverSity of Isfahan,Iran
>f.firoozbakht at sci.ui.ac.ir
>
>
>Quoting Leroy Quet <qqquet at mindspring.com>:
>>>...
>> If I did not make a mistake calculating the first few terms by hand,
>> here is a recursively-defined sequence which is not in the EIS yet.
>>
>> a[0] = 1;
>>
>> and for m >= 1,
>>
>> a[m] = sum{j=0 to a[m-1](mod m)} a[j]
>>
>> Ascii-art:
>> a[m-1](mod m)
>> ---
>> \
>> a[m] = / a[k]
>> ---
>> k=0
>>
>>
>> And, 0 <= a[m-1](mod m) <= m-1.
>>
>>...
Interesting.
I am slightly curious about such things such as:
for which indexes k, does a[k] = 1,
or when is a[k] < a[k-1] ?
And what would be the sequence of differences between consecutive k's,
where
a[k] < a[k-1]?
(The k's where a[k] = 1 are 0, 1, 4, and 64, for k < 100 {as seen from
the list generated by Farideh Firoozbakht}. These k's, except the 0, all
happen to be powers of 2; but this is much too small a sample to deduce
anything, obviously.)
Hmmm...I also wonder what the plot of this sequence, perhaps scaled
logarithmically, looks like.
Thank you,
Leroy Quet