login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102742 Elite primes: a prime number p is called elite if only a finite number of Fermat numbers 2^(2^n)+1 are quadratic residues mod p. 3
3, 5, 7, 41, 15361, 23041, 26881, 61441, 87041, 163841, 544001, 604801, 6684673, 14172161, 159318017, 446960641, 1151139841, 3208642561, 38126223361, 108905103361, 171727482881, 318093312001, 443069456129, 912680550401, 1295536619521, 1825696645121, 2061584302081 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Křížek, Luca, Shparlinski, & Somer show that a(n) >> n log^2 n. - Charles R Greathouse IV, Jan 25 2017

REFERENCES

Alexander Aigner; Über Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind. Monatsh. Math. 101 (1986), pp. 85-93

LINKS

Dennis Martin, Table of n, a(n) for n = 1..29

Alain Chaumont and Tom Mueller, All Elite Primes Up to 250 Billion, J. Integer Sequences, Vol. 9 (2006), Article 06.3.8.

Michal Křížek, Florian Luca, Igor E. Shparlinski, and Lawrence Somer, On the complexity of testing elite primes, Journal of Integer Sequences 14 (2011), Article 11.1.2, 5 pp.

Xiaoquin Li, Verifying Two Conjectures on Generalized Elite Primes, JIS 12 (2009) 09.4.7

Dennis Martin, Elite Prime Search

Dennis Martin, Elite Prime Search [Cached copy, with permission of author]

Dennis Martin, Elite and Anti-Elite Prime Search Methodology [Cached copy, with permission of author]

Tom Müller, Searching for large elite primes, Experimental Mathematics 15:2 (2006), 183-186.

Tom Muller, A. Reinhart, On generalized Elite Primes, JIS 11 (2008) 08.3.1

Tom Müller, On the Fermat Periods of Natural Numbers, J. Int. Seq. 13 (2010) # 10.9.5.

Tom Müller, On the Exponents of Non-Trivial Divisors of Odd Numbers and a Generalization of Proth's Primality Theorem, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.7.

CROSSREFS

Cf. A128852.

Sequence in context: A130536 A261511 A146972 * A089044 A117646 A064857

Adjacent sequences:  A102739 A102740 A102741 * A102743 A102744 A102745

KEYWORD

nonn

AUTHOR

Tom Mueller, Feb 08 2005; extended Jun 16 2005

EXTENSIONS

a(17) from Tom Mueller, Jul 20 2005

a(18)-a(21) from Tom Mueller, Apr 18 2006

6 further terms from Tom Mueller, Apr 16 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 18 18:07 EST 2018. Contains 318243 sequences. (Running on oeis4.)