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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A165255 Solinas primes; primes of the form p = 2^a +/- 2^b +/- 1 where 0 < b < a. 1

%I

%S 3,5,7,11,13,17,19,23,29,31,37,41,47,59,61,67,71,73,79,97,113,127,131,

%T 137,191,193,223,239,241,251,257,263,271,383,449,479,503,509,521,577,

%U 641,769,991,1009,1019,1021,1031,1033,1039,1087,1151,1153,1279,2017

%N Solinas primes; primes of the form p = 2^a +/- 2^b +/- 1 where 0 < b < a.

%C The primes not in the sequence are 43, 53, 83, 89, 101, 103, 107, 109, 139,... - _R. J. Mathar_, Sep 18 2009

%H Charles R Greathouse IV, <a href="/A165255/b165255.txt">Table of n, a(n) for n = 1..10000</a>

%H Jerome A. Solinas, <a href="http://www.cacr.math.uwaterloo.ca/techreports/1999/corr99-39.pdf">Generalized Mersenne numbers</a> (1999)

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Solinas_prime">Solinas prime</a>

%F Trivially, a(n) >> exp(sqrt(2n)). - _Charles R Greathouse IV_, Dec 04 2012

%e 3 = 2^3 - 2^2 - 1.

%e 5 = 2^3 - 2^2 + 1.

%e 7 = 2^4 - 2^3 - 1.

%e 11 = 2^3 + 2^2 - 1.

%e 13 = 2^3 + 2^2 + 1.

%e 17 = 2^5 - 2^4 + 1.

%e 19 = 2^4 + 2^2 - 1.

%e 23 = 2^4 + 2^3 - 1.

%o (PARI) go(n)=my(v=List(),ta,tb);for(a=2,n,ta=2^a;tb=1;for(b=1,a-1,tb<<=1;if(ispseudoprime(ta+tb+1),listput(v,ta+tb+1));if(ispseudoprime(ta+tb-1),listput(v,ta+tb-1));if(ispseudoprime(ta-tb+1),listput(v,ta-tb+1));if(ispseudoprime(ta-tb-1),listput(v,ta-tb-1))));vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Dec 04 2012

%K nonn

%O 1,1

%A _Paul Muljadi_, Sep 11 2009

%E More terms from _Max Alekseyev_ and _R. J. Mathar_, Sep 17 2009

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 March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)