A122716 Primes of the form p^2 + q^10 where p and q are primes.

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..34.

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: A283724 A168225 A282576 * A031609 A236804 A023063

Adjacent sequences: A122713 A122714 A122715 * A122717 A122718 A122719

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 23 2006

Extensions

More terms from Robert G. Wilson v, Sep 26 2006

Status

approved