OFFSET
1,1
COMMENTS
Removed redundant mod(p,4) = 1 criterion from definition. By quadratic reciprocity, all factors of 1 + 4Q^2 are congruent to 1 (mod 4). See comments at the end of the b-file for an additional eight terms not proved, but nevertheless highly likely to be correct. - Daran Gill, Mar 23 2013
REFERENCES
P. G. L. Dirichlet (1871): Vorlesungen über Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 13.
LINKS
Daran Gill, Table of n, a(n) for n = 1..33
Mersenne Forum, Sequence A057207
OEIS wiki, OEIS sequences needing factors
EXAMPLE
a(4)=53 is the smallest prime divisor of 4*(5.101.1020101)^2+1 = 1061522231810040101 = 53*1613*12417062216309.
MATHEMATICA
t = {5}; Do[q = Times @@ t; AppendTo[t, FactorInteger[1 + 4*q^2][[1, 1]]], {6}]; t (* T. D. Noe, Mar 27 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 09 2000
EXTENSIONS
Eight more terms, a(9)-a(16), from Max Alekseyev, Apr 27 2009
Seventeen more terms, a(17)-a(33), added by Daran Gill, Mar 23 2013
STATUS
approved