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A144255
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Semiprimes of the form n^2+1.
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3
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10, 26, 65, 82, 122, 145, 226, 362, 485, 626, 785, 842, 901, 1157, 1226, 1522, 1765, 1937, 2026, 2117, 2305, 2402, 2501, 2602, 2705, 3365, 3482, 3601, 3722, 3845, 4097, 4226, 4762, 5042, 5777, 6085, 6242, 6401, 7226, 7397, 7745, 8465, 9026, 9217, 10001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Iwaniec proves that there are an infinite number of semiprimes or primes of the form n^2+1. Because n^2+1 is not a square for n>0, all such semiprimes have two distinct prime factors.
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REFERENCES
| Iwaniec, H., "Almost primes represented by quadratic polynomials", Invent. math. 47, 1978, 171-188.
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LINKS
| Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n)=A085722(n)^2+1.
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PROG
| (PARI) select(vector(500, n, n^2+1), n->bigomega(n)==2)
\\ Zak Seidov Feb 24 2011
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CROSSREFS
| Cf. A001358, A085722.
Sequence in context: A125075 A055710 A134420 * A072379 A005970 A192254
Adjacent sequences: A144252 A144253 A144254 * A144256 A144257 A144258
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KEYWORD
| nonn,easy
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 16 2008
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