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A122715
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Primes of the form p^2 + q^9 where p and q are primes.
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0
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521, 19687, 40353611, 27206534396294951, 58871586708267917, 977752464192721105849427, 1733003264116942402576542827, 24847921085939626319928324473, 114264841877247135195655381697
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OFFSET
| 1,1
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COMMENTS
| 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.
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FORMULA
| {a(n)} = {p^2 + q^9 in A000040 where p and q are in A000040}.
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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.
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MATHEMATICA
| s = {521}; Do[ pq = Prime@p^9 + 4; If[ PrimeQ@pq, AppendTo[s, pq]], {p, 300}]; s (* Robert G. Wilson v *)
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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 * A153180 A015291 A028484
Adjacent sequences: A122712 A122713 A122714 * A122716 A122717 A122718
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006
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EXTENSIONS
| More terms from Robert G. Wilson v Sep 26 2006
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