A165255 Solinas primes; primes of the form p = 2^a +/- 2^b +/- 1 where 0 < b < a.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 59, 61, 67, 71, 73, 79, 97, 113, 127, 131, 137, 191, 193, 223, 239, 241, 251, 257, 263, 271, 383, 449, 479, 503, 509, 521, 577, 641, 769, 991, 1009, 1019, 1021, 1031, 1033, 1039, 1087, 1151, 1153, 1279, 2017

Offset

1,1

Comments

The primes not in the sequence are 43, 53, 83, 89, 101, 103, 107, 109, 139,... - R. J. Mathar, Sep 18 2009

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Jerome A. Solinas, Generalized Mersenne numbers (1999)

Wikipedia, Solinas prime

Formula

Trivially, a(n) >> exp(sqrt(2n)). - Charles R Greathouse IV, Dec 04 2012

Example

3 = 2^3 - 2^2 - 1.
5 = 2^3 - 2^2 + 1.
7 = 2^4 - 2^3 - 1.
11 = 2^3 + 2^2 - 1.
13 = 2^3 + 2^2 + 1.
17 = 2^5 - 2^4 + 1.
19 = 2^4 + 2^2 - 1.
23 = 2^4 + 2^3 - 1.

Prog

(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

Crossrefs

Sequence in context: A020615 A172146 A225670 * A223036 A155058 A007703

Adjacent sequences: A165252 A165253 A165254 * A165256 A165257 A165258

Keyword

nonn

Author

Paul Muljadi, Sep 11 2009

Extensions

More terms from Max Alekseyev and R. J. Mathar, Sep 17 2009

Status

approved