[seqfan] sequence of "almost totatives" of primorial Pn
Jamie Morken
jmorken at shaw.ca
Thu May 11 00:53:39 CEST 2017
Hi,I was working on an algorithm to find the totatives of a given Pn and was wondering if the algorithmand resultant sequence is of interest for an OEIS sequence. Here's the algorithm and the sequence,I apologize for my math terminology errors!
algorithm to find primorial totatives:
start with known Pn and totatives, ie Pn(2)=2*3=6, with totatives 1,5
find Pn(2+1)=30 next prime factor j = 5
for each Pn(2) totative 1,5 add Pn(2)=6 to the totative j-1=4 times, giving a table with j rows
result:
1 5
7 11
13 17
19 23
25 29
multiply Pn(2) totatives 1,5 with j=5
result:
totative 1 1*5=5
totative 5 5*5=25
remove these values 5,25 from the previous results, the count of values to remove is the count of totatives in Pn(2), 2
result:
1 11
7 17
13 23
19 29
These are the totatives of Pn(2+1)=Pn(3)=30
To find the Pn(4) totatives, do the same above steps, ie first
find Pn(3+1)=210 next prime factor j = 7 then make the table with one column for each Pn3 totative (8 columns)
and remove the non-totatives like above, and make a table with j rows. The count of values to remove is the
count of totatives in Pn(3), 8
Idea for OEIS sequence is the removed values ie start of sequence is 5,25
new OEIS sequence to make from this: [5,25],[7,49,77,91,119,133,161,203],[48terms],[480terms],[5760terms]...
["almost totatives" divisible by 5,7,11, (successive primes) in each set of brackets corresponding to consecutive primorials set of "almost totatives"]
or OEIS sequence of these values sorted.cheers,Jamie
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