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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
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
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 March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)