|
Search: id:A057204
|
|
|
| A057204 |
|
Primes congruent to 1 mod 6 generated recursively. Initial prime is 7. The next term is p(n)=Min {p is prime; p divides 4Q^2+3; Mod[p,6]=1}, where Q is the product of previous entries of the sequence. |
|
+0
27
|
|
| 7, 199, 7761799, 487, 67, 103, 3562539697, 7251847, 13, 127, 5115369871402405003, 31, 697830431171707, 151, 3061, 229, 193
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
4Q^2+3 always has a prime divisor congruent to 1 modulo 6.
|
|
REFERENCES
|
Dirichlet,P.G.L (1871): Vorlesungen uber 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.
|
|
EXAMPLE
|
a(4)=487 is the smallest prime divisor of 4QQ+3=10812186007, congruent to 1 mod 6, where Q=7.199.7761799.
|
|
CROSSREFS
|
Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002476, A057204-A057208.
Sequence in context: A157388 A068233 A154936 this_sequence A124988 A128680 A157775
Adjacent sequences: A057201 A057202 A057203 this_sequence A057205 A057206 A057207
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Oct 09 2000
|
|
EXTENSIONS
|
More terms from Nick Hobson Nov 14 2006
|
|
|
Search completed in 0.002 seconds
|
