|
| |
|
|
A237819
|
|
Number of primes p < n such that floor(sqrt(n-p)) is a Sophie Germain prime.
|
|
1
|
|
|
|
0, 0, 0, 0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 6, 6, 6, 7, 6, 7, 7, 7, 6, 7, 6, 6, 7, 7, 5, 6, 5, 6, 6, 6, 4, 4, 4, 5, 5, 5, 5, 6, 5, 6, 5, 5, 6, 7, 6, 6, 6, 6, 5, 6, 5, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,7
|
|
|
COMMENTS
|
Conjecture: (i) a(n) > 0 for all n > 5.
(ii) For any integer n > 10, there is a prime p < n such that q = floor(sqrt(n-p)) and q + 2 are both prime.
|
|
|
LINKS
|
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
|
|
|
EXAMPLE
|
a(6) = 1 since 2, floor(sqrt(6-2)) = 2 and 2*2 + 1 = 5 are all prime.
|
|
|
MATHEMATICA
|
f[n_]:=Floor[Sqrt[n]]
q[n_]:=PrimeQ[f[n]]&&PrimeQ[2*f[n]+1]
a[n_]:=Sum[If[q[n-Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}]
Table[a[n], {n, 1, 80}]
|
|
|
CROSSREFS
|
Cf. A000040, A001359, A005384, A006512, A237720, A237721, A237815, A237817.
Sequence in context: A123087 A071868 A179390 * A082447 A139789 A000720
Adjacent sequences: A237816 A237817 A237818 * A237820 A237821 A237822
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Zhi-Wei Sun, Feb 13 2014
|
|
|
STATUS
|
approved
|
| |
|
|
