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A045700
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Primes of form p^2+q^3 where p and q are primes.
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10
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17, 31, 347, 6863, 493043, 1092731, 1295033, 21253937, 22665191, 38272757, 54439943, 115501307, 904231067, 1121622323, 2738124203, 3067586681, 3301293173, 3673650011, 4549540397, 4599141251, 6507781367, 7222633241
(list; graph; refs; listen; history; internal format)
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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. If q=2 then we want primes of form p^2+8. But 8=-1 mod 3. Since p is prime, p=3 or == 1 or 2 mod 3. If p=1 or 2 mod 3 then 3|p^2+8, so p=3. Therefore with the exception of the first entry (3^2+8=17) this sequence is really just primes of the form q^3+4.
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LINKS
| Ray Chandler, Table of n, a(n) for n = 1..10000
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FORMULA
| Primes in A045699.
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EXAMPLE
| a(4) = 6863 = 19^3 + 2^2.
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MAPLE
| for n from 1 to 1000 do if (isprime((ithprime(n))^3+4)) then print((ithprime(n))^3+4, 4); fi; if (isprime((ithprime(n))^2+8)) then print((ithprime(n))^2+8, 8); fi; od;
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MATHEMATICA
| Join[{17}, Select[Prime[Range[300]]^3+4, PrimeQ]] (* From Harvey P. Dale, Jul 20 2011 *)
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CROSSREFS
| Cf. A045699.
Sequence in context: A163443 A027722 A060342 * A146800 A146731 A146667
Adjacent sequences: A045697 A045698 A045699 * A045701 A045702 A045703
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KEYWORD
| nice,nonn,easy
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AUTHOR
| Felice Russo (frusso(AT)micron.com)
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EXTENSIONS
| Extension and comment from Joe DeMaio (jdemaio(AT)kennesaw.edu)
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