|
Search: id:A045700
|
|
|
| A045700 |
|
Primes of form p^2+q^3 where p and q are primes. |
|
+0
8
|
|
| 17, 31, 347, 6863, 493043, 1092731, 1295033, 21253937, 22665191, 38272757, 54439943, 115501307, 904231067, 1121622323, 2738124203, 3067586681, 3301293173, 3673650011, 4549540397, 4599141251, 6507781367, 7222633241
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
p and q cannot both be odd. Thus p=2 or q=2. If q=2 then we want primes of form p^2+8. But 8=-1 mod 3. Since p is prime, p=3 or == 1 or 2 mod 3. If p=1 or 2 mod 3 then 3|p^2+8, so p=3. Therefore with the exception of the first entry (3^2+8=17) this sequence is really just primes of the form q^3+4.
|
|
FORMULA
|
For example: 6863=19^3+2^2.
|
|
MAPLE
|
for n from 1 to 1000 do if (isprime((ithprime(n))^3+4)) then print((ithprime(n))^3+4, 4); fi; if (isprime((ithprime(n))^2+8)) then print((ithprime(n))^2+8, 8); fi; od;
|
|
CROSSREFS
|
Cf. A045699.
Sequence in context: A163443 A027722 A060342 this_sequence A146800 A146731 A146667
Adjacent sequences: A045697 A045698 A045699 this_sequence A045701 A045702 A045703
|
|
KEYWORD
|
nice,nonn,easy
|
|
AUTHOR
|
Felice Russo (felice.russo(AT)katamail.com)
|
|
EXTENSIONS
|
Extension and comment from Joe DeMaio (jdemaio(AT)kennesaw.edu)
|
|
|
Search completed in 0.002 seconds
|
