[seqfan] Re: New sequence
Neil Fernandez
primeness at borve.org
Thu Apr 6 14:22:03 CEST 2017
Hi,
Graeme McRae wrote:
> I also looked for even numbers such that *all* the values E+pn are
> prime. The only such even numbers I found smaller than 1000 were 8 and
> 12. In fact, the only even numbers smaller than 1000 such that all but
> one of the values E+pn are prime are 8, 12, 18, 24, and 30.
The only prime pair summing to 8 is {5,3}, and 8 + {5,3} are both prime.
-"- summing to 12 is {5,7}, and 12 + {5,7} are both prime.
10 is not on the list if we count the summands with multiplicity
({3,5,5,7}) but it is if we don't. The same is true for 6.
I get
(6, 10,) 18, 24, 30
for E < 20000.
Another nice sequence is
a(n):= the number of pairs of primes {p_1, p_2} that sum to 2n and for
which 2n+p_1 and 2n+p_2 are both prime.
For this I get
0,0,0,2,2,2,1,2,3,2,1,5,1,0,1,0,5,1,1,5,0,1,6,...
And the numbers for which a(n/2) is a maximum run
8, 18, 24, 42, 60, 90, 120, 210, 330, 420, 630, 840, 1050, 1260, 1470,
1680, 1890
Neil
--
Neil Fernandez
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