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A080149
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Numbers n such that n^2+1 and n^2+3 are both prime.
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3
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2, 4, 10, 14, 74, 94, 130, 134, 146, 160, 230, 256, 326, 340, 350, 406, 430, 440, 470, 584, 634, 686, 700, 704, 784, 860, 920, 986, 1054, 1070, 1156, 1210, 1324, 1340, 1354, 1366, 1394, 1420, 1456, 1460, 1564, 1700, 1784, 1816, 1876, 2006, 2080, 2096, 2174
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Hardy and Littlewood conjecture that this sequence is infinite. This sequence is the intersection of A005574 (n such that n^2+1 is prime) and A049422 (n such that n^2+3 is prime).
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REFERENCES
| P. Ribenboim, "The New Book of Prime Number Records," Springer-Verlag, 1996, p. 408.
G. H. Hardy and J. E. Littlewood, "Some problems of `partitio numerorum'; III: on the expression of a number as a sum of primes," Acta Mathematica, Vol. 44, pp. 1-70, 1923.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Zak Seidov, Table of n, a(n) for n=1..32898, a(n)<10^7
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FORMULA
| Conjecture : a(n) is asymptotic to c*n*log(n)^2 with c around 2.9... - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 16 2004
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EXAMPLE
| 10 is in this sequence because 101 and 103 are both prime.
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MATHEMATICA
| lst={}; Do[If[PrimeQ[m^2+1]&&PrimeQ[m^2+3], AppendTo[lst, m]], {m, 3000}]; lst
okQ[n_]:=Module[{n2=n^2}, PrimeQ[n2+1]&&PrimeQ[n2+3]]; Select[Range[2200], okQ] (* From Harvey P. Dale, Apr 21 2011 *)
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PROG
| (PARI) isA080149(n) = isprime(n^2+1) && isprime(n^2+3) [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Mar 22 2010]
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CROSSREFS
| Cf. A005574, A049422.
Sequence in context: A082230 A078775 A056392 * A128513 A048200 A064513
Adjacent sequences: A080146 A080147 A080148 * A080150 A080151 A080152
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jan 30 2003
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