A122617 Primes of the form p^3 + q^4 where p and q are primes.

43, 89, 359, 2213, 300779, 4330763, 13997537, 36264707, 49430879, 62570789, 223648559, 251239607, 393832853, 423564767, 620650493, 746142659, 973242287, 1102302953, 1160935667, 1284365519, 1393668629, 1784770613, 1892819069, 3261545603, 4306878899

Offset

1,1

Comments

p and q cannot both be odd. Thus p=2 or q=2. Except for 2^3 + 3^4 = 89, all such primes are of the form 2^4 + q^3.

Links

Table of n, a(n) for n=1..25.

Formula

{a(n)} = {p^3 + q^4 in A000040 where p and q are in A000040}.

Example

a(1) = 2^4 + 3^3 = 43.
a(2) = 2^3 + 3^4 = 89.
a(3) = 2^4 + 7^3 = 359.
a(4) = 2^4 + 13^3 = 2213.
a(5) = 2^4 + 67^3 = 300779.
a(6) = 2^4 + 163^3 = 4330763.
a(7) = 2^4 + 241^3 = 13997537.

Mathematica

upto=45*10^9; With[{c=PrimePi[Ceiling[Power[upto-16, (3)^-1]]]}, Sort[ Join[ {89}, Select[#+16&/@(Prime[Range[2, c]]^3), PrimeQ]]]] (* Harvey P. Dale, Jul 08 2011 *)

Crossrefs

Cf. A000040, A045700 Primes of form p^2+q^3 where p and q are primes.

Sequence in context: A108394 A288641 A141924 * A306114 A044181 A044562

Adjacent sequences: A122614 A122615 A122616 * A122618 A122619 A122620

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 21 2006

Extensions

More terms from Harvey P. Dale, Jul 07 2011

Status

approved