[seqfan] Re: sequence of "almost totatives" of primorial Pn
Jamie Morken
jmorken at shaw.ca
Tue May 16 09:44:25 CEST 2017
Hi,
Thanks for the code! I'll try sorting the output to get all values up to 1000 or so, would require up to the
second term in Pn(11) ie 31^2 =961, then all later terms should be > 1000 except for the remaining prime numbers > 31 I think.
Here's a definition for the sequence maybe:
For each primorial p, take the product for each totative in p with the prime factor in p+1 not in p.
ie for Pn(3)=30, Pn(3+1) prime factor=7, Pn(3) totatives=1,7,11,13,17,19,23,29
7*1=7
7*7=49
7*11=77
7*13=91
7*17=119
7*19=133
7*23=161
7*29=203
That gives the sequence in the second group in the brackets
{7, 49, 77, 91, 119, 133, 161, 203}
cheers,
Jamie
----- Original Message -----
From: L. Edson Jeffery <lejeffery2 at gmail.com>
To: seqfan at list.seqfan.eu
Sent: Mon, 15 May 2017 12:38:18 -0600 (MDT)
Subject: [seqfan] Re: sequence of "almost totatives" of primorial Pn
Hello Jamie,
Not sure if your sequence is of any value for the database, but the
following Mathematica code (likely not optimal) generates it:
p[n_] := Product[Prime[k], {k, n - 1}];
a[n_] := a[n] = Prime[n + 1]*t[n];
t[n_] := t[n] =
If[n == 2, {1, 5},
Complement[
Flatten[Table[k*p[n] + t[n - 1], {k, 0, Prime[n] - 1}]],
a[n - 1]]];
Table[a[n], {n, 2, 4}]
{{5, 25}, {7, 49, 77, 91, 119, 133, 161, 203}, {11, 121,
143, 187, 209, 253, 319, 341, 407, 451, 473, 517, 583, 649, 671,
737, 781, 803, 869, 913, 979, 1067, 1111, 1133, 1177, 1199, 1243,
1331, 1397, 1441, 1507, 1529, 1573, 1639, 1661, 1727, 1793, 1837,
1859, 1903, 1969, 1991, 2057, 2101, 2123, 2167, 2189, 2299}}
Ed Jeffery
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