OFFSET
1,1
COMMENTS
2+Q^2 always has a prime divisor congruent to 3 modulo 8.
REFERENCES
D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 191.
LINKS
Robert Price, Table of n, a(n) for n = 1..15
N. Hobson, Home page (listed in lieu of email address)
EXAMPLE
a(3) = 1091 is the smallest prime divisor congruent to 3 mod 8 of 2+Q^2 = 1091, where Q = 3 * 11.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Nick Hobson, Nov 18 2006
EXTENSIONS
a(10) from Robert Price, Jul 04 2015
a(11) from Robert Price, Jul 05 2015
STATUS
approved