|
Search: id:A122716
|
|
|
| A122716 |
|
Primes of the form p^2 + q^10 where p and q are primes. |
|
+0
1
|
|
| 1033, 1049, 1193, 1553, 2393, 3833, 6353, 10433, 11633, 12473, 19793, 25673, 38273, 50753, 52553, 55313, 59053, 67073, 95273, 98993, 101513, 114593, 158633, 197273, 215393, 300233, 376793, 381713, 427433, 459353, 553073, 620393, 735473, 787793
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
p and q cannot both be odd. Thus p=2 or q=2. There are rarer primes of the form 2^2 + q^10 such as 2^2 + 3^10 = 59053 and 2^2 + 5^10 = 9765629 and 2^2 + 13^10 = 137858491853. Hence most solutions are of the form 2^10 + q^2, and (except for rarer solutions such as 5^2 + 2^10 = 1049 and 2^2 + 5^10 = 9765629, no more with the larger prime under 100) are congruent to 3 mod 10.
|
|
FORMULA
|
{a(n)} = {p^2 + q^10 in A000040 where p and q are in A000040}.
|
|
EXAMPLE
|
a(1) = 3^2 + 2^10 = 1033.
a(2) = 5^2 + 2^10 = 1049.
a(3) = 13^2 + 2^10 = 1193.
a(4) = 23^2 + 2^10 = 1553.
|
|
MATHEMATICA
|
Take[Select[Sort[Table[Prime@p^2 + Prime@q^10, {p, 200}, {q, 3}] // Flatten], PrimeQ@# &], 34] - Robert G. Wilson v Sep 26 2006
|
|
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: A061327 A023062 A035046 this_sequence A023063 A023087 A025412
Adjacent sequences: A122713 A122714 A122715 this_sequence A122717 A122718 A122719
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 23 2006
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v Sep 26 2006
|
|
|
Search completed in 0.002 seconds
|
