|
|
A066436
|
|
Primes of the form 2*n^2 - 1.
|
|
48
|
|
|
7, 17, 31, 71, 97, 127, 199, 241, 337, 449, 577, 647, 881, 967, 1151, 1249, 1567, 2311, 2591, 2887, 3041, 3361, 3527, 3697, 4049, 4231, 4801, 4999, 5407, 6271, 6961, 7687, 7937, 8191, 9521, 10657, 11551, 12799, 13121, 14449, 15137, 16561
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
It is conjectured that this sequence is infinite.
Also primes p such that 8p + 8 is a square. - Cino Hilliard, Dec 18 2003
Also primes p such that 2p+2 is square; also primes p such that (p+1)/2 is square. - Ray Chandler, Sep 15 2005
Arithmetic numbers which are squares, A003601(p)=A000290(k), p prime, k integer. sigma_1(p)/sigma_0(p)=k^2; p prime, k integer. - Ctibor O. Zizka, Jul 14 2008
|
|
REFERENCES
|
D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.
|
|
LINKS
|
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [ p: n in [1..100] | IsPrime(p) where p is 2*n^2-1 ]; // Klaus Brockhaus, Dec 29 2008
(PARI) { n=0; for (m=1, 10^9, p=2*m^2 - 1; if (isprime(p), write("b066436.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 14 2010
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|