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A165255 Solinas primes; primes of the form p = 2^a +/- 2^b +/- 1 where 0 < b < a. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified December 4 19:31 EST 2016. Contains 278755 sequences.