|
| |
|
|
A066436
|
|
Primes of the form 2*n^2 - 1.
|
|
34
| |
|
|
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; 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 (hillcino368(AT)gmail.com), Dec 18 2003
Also primes p such that 2p+2 is square; also primes p such that (p+1)/2 is square. - Ray Chandler (rayjchandler(AT)sbcglobal.net), 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 (ctibor.zizka(AT)seznam.cz), Jul 14 2008
|
|
|
REFERENCES
| D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
|
|
|
MATHEMATICA
| lst={}; Do[p=2*n^2-1; If[PrimeQ[p], AppendTo[lst, p]], {n, 9^3}]; lst...or/and... lst={}; Do[p=ChebyshevT[2, n]; If[PrimeQ[p], AppendTo[lst, p]], {n, 9^3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
|
|
|
PROG
| (MAGMA) [ p: n in [1..100] | IsPrime(p) where p is 2*n^2-1 ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 14 2010]
|
|
|
CROSSREFS
| See A066049 for the values of n, see A091176 for prime index. Cf. A090697, A110558.
Cf. A003601, A000290.
Sequence in context: A024835 A178491 A144861 * A128002 A074275 A051411
Adjacent sequences: A066433 A066434 A066435 * A066437 A066438 A066439
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 09 2002
|
| |
|
|
