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A124984
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Primes of the form 8*k + 3 generated recursively. Initial prime is 3. General term is a(n) = Min_{p is prime; p divides 2 + Q^2; p == 3 (mod 8)}, where Q is the product of previous terms in the sequence.
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19
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3, 11, 1091, 1296216011, 2177870960662059587828905091, 76870667, 19, 257680660619, 73677606898727076965233531, 23842300525435506904690028531941969449780447746432390747, 35164737203
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OFFSET
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1,1
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COMMENTS
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2+Q^2 always has a prime divisor congruent to 3 modulo 8.
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REFERENCES
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D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 191.
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LINKS
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Robert Price, Table of n, a(n) for n = 1..15
N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
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a(3) = 1091 is the smallest prime divisor congruent to 3 mod 8 of 2+Q^2 = 1091, where Q = 3 * 11.
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MATHEMATICA
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a = {3}; q = 1;
For[n = 2, n ≤ 5, n++,
q = q*Last[a];
AppendTo[a, Min[Select[FactorInteger[2 + q^2][[All, 1]], Mod[#,
8] \[Equal] 3 &]]];
];
a (* Robert Price, Jul 14 2015 *)
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PROG
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(PARI) lista(nn) = my(f, q=3); print1(q); for(n=2, nn, f=factor(2+q^2)[, 1]~; for(i=1, #f, if(f[i]%8==3, print1(", ", f[i]); q*=f[i]; break))); \\ Jinyuan Wang, Aug 05 2022
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CROSSREFS
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Cf. A000945, A007520, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A088579 A344946 A006938 * A287432 A353085 A034797
Adjacent sequences: A124981 A124982 A124983 * A124985 A124986 A124987
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KEYWORD
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nonn
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AUTHOR
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Nick Hobson, Nov 18 2006
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EXTENSIONS
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a(10) from Robert Price, Jul 04 2015
a(11) from Robert Price, Jul 05 2015
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STATUS
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approved
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