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Search: id:A122715
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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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| 521, 19687, 40353611, 27206534396294951, 58871586708267917, 977752464192721105849427, 1733003264116942402576542827, 24847921085939626319928324473, 114264841877247135195655381697
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OFFSET
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1,1
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COMMENT
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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
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{a(n)} = {p^2 + q^9 in A000040 where p and q are in A000040}.
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EXAMPLE
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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
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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
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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.
Adjacent sequences: A122712 A122713 A122714 this_sequence A122716 A122717 A122718
Sequence in context: A004928 A004948 A138063 this_sequence A015291 A028484 A057699
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 23 2006
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EXTENSIONS
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More terms from Robert G. Wilson v Sep 26 2006
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