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A124986
Primes of the form 12*k + 5 generated recursively. Initial prime is 5. General term is a(n) = Min_{p is prime; p divides 1 + 4*Q^2; p == 5 (mod 12)}, where Q is the product of previous terms in the sequence.
1
5, 101, 1020101, 53, 29, 2507707213238852620996901, 449, 433361, 401, 925177698346131180901394980203075088053316845914981, 44876921, 17, 173
OFFSET
1,1
COMMENTS
All prime divisors of 1+4Q^2 are congruent to 1 modulo 4.
At least one prime divisor of 1+4Q^2 is congruent to 2 modulo 3 and hence to 5 modulo 12.
The first seven terms are the same as those of A057207.
The next term is known but is too large to include.
LINKS
EXAMPLE
a(8) = 433361 is the smallest prime divisor congruent to 5 mod 12 of 1+4Q^2 = 3179238942812523869898723304484664524974766291591037769022962819805514576256901 = 13 * 433361 * 42408853 * 2272998442375593325550634821 * 5854291291251561948836681114631909089, where Q = 5 * 101 * 1020101 * 53 * 29 * 2507707213238852620996901 * 449.
MATHEMATICA
a={5}; q=1;
For[n=2, n<=5, n++,
q=q*Last[a];
AppendTo[a, Min[Select[FactorInteger[4*q^2+1][[All, 1]], Mod[#, 12]==5 &]]];
];
a (* Robert Price, Jul 16 2015 *)
KEYWORD
nonn
AUTHOR
Nick Hobson, Nov 18 2006 and Nov 23 2006
STATUS
approved