A124989 Primes of the form 10*k + 9 generated recursively. Initial prime is 19. General term is a(n) = Min_{p is prime; p divides 100*Q^2 - 5; p == 9 (mod 10)}, where Q is the product of previous terms in the sequence.

19, 7219, 462739, 509, 129229, 295380580489, 9653956849, 149, 110212292237172705230749846071050188009093377022084806290042881946231583507557298889, 157881589, 60397967745386189, 1429, 79

Offset

1,1

Comments

100Q^2-5 always has a prime divisor congruent to 9 modulo 10.

Links

Robert Price, Table of n, a(n) for n = 1..14

Example

a(3) = 462739 is the smallest prime divisor congruent to 9 mod 10 of 100Q^2-5 = 1881313992095 = 5 * 462739 * 813121, where Q = 19 * 7219.

Mathematica

a={19}; q=1;
For[n=2, n<=6, n++,
    q=q*Last[a];
    AppendTo[a, Min[Select[FactorInteger[100*q^2-5][[All, 1]], Mod[#, 10]==9&]]];
    ];
a (* Robert Price, Jul 18 2015 *)

Crossrefs

Cf. A000945, A030433, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Sequence in context: A013724 A067267 A340165 * A265964 A156973 A270972

Adjacent sequences: A124986 A124987 A124988 * A124990 A124991 A124992

Keyword

nonn

Author

Nick Hobson, Nov 18 2006

Status

approved