|
Search: id:A122715
|
|
|
| A122715 |
|
Primes of the form p^2 + q^9 where p and q are primes. |
|
+0
1
|
|
| 521, 19687, 40353611, 27206534396294951, 58871586708267917, 977752464192721105849427, 1733003264116942402576542827, 24847921085939626319928324473, 114264841877247135195655381697
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
p and q cannot both be odd. Thus p=2 or q=2. There are no primes of the form 2^9 + q^2 other than 3^2 + 2^9 = 521. Hence all solutions are of the form 2^2 + q^9.
|
|
FORMULA
|
{a(n)} = {p^2 + q^9 in A000040 where p and q are in A000040}.
|
|
EXAMPLE
|
a(1) = 3^2 + 2^9 = 521.
a(2) = 2^2 + 3^9 = 19687.
a(3) = 2^2 + 7^9 = 40353611.
a(4) = 2^2 + 67^9 = 27206534396294951.
a(5) = 2^2 + 73^9 = 58871586708267917.
a(6) = 2^2 + 453^9 = 803311192691904837821737.
|
|
MATHEMATICA
|
s = {521}; Do[ pq = Prime@p^9 + 4; If[ PrimeQ@pq, AppendTo[s, pq]], {p, 300}]; s (* Robert G. Wilson v *)
|
|
CROSSREFS
|
Cf. A000040, A045700 Primes of form p^2+q^3 where p and q are prime, A122617 Primes of form p^3+q^4 where p and q are primes.
Sequence in context: A004948 A138063 A167734 this_sequence A153180 A015291 A028484
Adjacent sequences: A122712 A122713 A122714 this_sequence A122716 A122717 A122718
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v Sep 26 2006
|
|
|
Search completed in 0.002 seconds
|
