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A108814
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Numbers n such that n^4 + 4 is semiprime.
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1
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3, 5, 15, 25, 55, 125, 205, 385, 465, 635, 645, 715, 1095, 1145, 1175, 1245, 1275, 1315, 1375, 1565, 1615, 1675, 1685, 1965, 2055, 2085, 2095, 2405, 2455, 2535, 2665, 2835, 2925, 3135, 3305, 3535, 3755, 3775, 4025, 4155, 4175, 4365, 4605, 4615, 4735, 4785
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Except for the first, all the terms above generate brilliant numbers.
Numbers n such that n - 1 + i and n + 1 + i are (twin) Gaussian primes, see Shanks. [Charles R Greathouse IV, Apr 20, 2011]
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REFERENCES
| Daniel Shanks, "A Note on Gaussian Twin Primes", Mathematics of Computation 14:70 (1960), pp. 201-203.
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PROG
| (PARI) forstep(n=1, 1e5, 2, if(isprime(n^2-2*n+2)&isprime(n^2+2*n+2), print1(n", "))) \\ Charles R Greathouse IV, Apr 20, 2011
(MAGMA IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [1..5000] | IsSemiprime(n^4+4)]; // Vincenzo Librandi, Apr 20 2011
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CROSSREFS
| Sequence in context: A146835 A146795 A166479 * A018272 A018421 A056487
Adjacent sequences: A108811 A108812 A108813 * A108815 A108816 A108817
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KEYWORD
| nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jul 10 2005
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