A091902 is duplicate of A067698

[Max Alekseyev]

SeqFan

A091902 is a duplicate of A067698. They differ only with an extra
first term 1 in A091902, which actually should not be there since
log(log(n)) in not defined for n=1.
A067698 is much developed than A091902, missing only a link to Robin's
Theorem. So, I suggest to add a link to Robin's Theorem to A067698 and
remove A091902 from OEIS.

Max



I have recently submitted these sequences, which have already appeared in 
the database.

>%I A131789
>%S A131789 1,2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,3,1
>%N A131789 a(n) = the length of the nth run of similar consecutive values 
>in the sequence A000005. (A000005(n) = the number of positive divisors of n.)
>%e A131789 Runs of sequence A000005: (1), (2,2), (3), (2), (4), (2), (4), 
>(3), (4), (2), (6), (2), (4,4), (5), (2), (6), (2), (6), (4,4), (2), (8), 
>(3),...
>%Y A131789 A000005,A131790
>%O A131789 1
>%K A131789 ,more,nonn,


>%I A131790
>%S A131790 1,1,10,1,5,1,3,1,5,1
>%N A131790 a(n) = the length of the nth run of similar consecutive values 
>in the sequence A131789.
>%e A131790 Runs of sequence A131789: (1), (2), (1,1,1,1,1,1,1,1,1,1), (2), 
>(1,1,1,1,1), (2), (1,1,1), (2), (1,1,1,1,1,), (3),...
>%Y A131790 A000005,A131789
>%O A131790 1
>%K A131790 ,more,nonn,


It seems VERY likely to me that there is no infinite string of 1's, or of 
anything else, in sequence A131789 (ie. the terms of A131790 are all 
finite).

Can it be PROVED that all terms of A131790 are finite, possibly using 
Hardy and Wright or some other such reference?

A harder question to answer:
We can define sequence S(m) = {s(m,n)}, where s(m,n) = the length of the 
nth run of similar consecutive values in the sequence S(m-1), where S(0) 
= sequence A000005.
(And S(1) = A131789, S(2) = A131790, of course.)

Is every term of S(m) finite for every m = positive integer?

It seems intuitive obvious that, yes, all terms are finite. But a proof 
would be harder to produce.


Thanks,
Leroy Quet