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Numbers n such that 2^n - 2^((n + 1)/2) + 1 is prime.
(Formerly M2703)
7

%I M2703 #28 Jun 17 2020 02:23:36

%S 3,7,47,73,79,113,151,167,239,241,353,367,457,1367,3041,27529,49207,

%T 160423,364289,991961,1203793,1667321,4792057

%N Numbers n such that 2^n - 2^((n + 1)/2) + 1 is prime.

%C If A007670 is a proper subset of A057429, then 364289 & 991961 are the next two terms.

%D J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. Brillhart, <a href="http://dx.doi.org/10.1090/S0025-5718-1962-0148593-0">Concerning the number 2^(2p)+1, p prime</a>, Math. Comp. 16 (80) (1962) 424-430.

%H J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>

%o (PARI) is(n)=isprime(2^n-2^((n+1)/2)+1) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A006598.

%K nonn,hard,more

%O 1,1

%A _N. J. A. Sloane_, _Robert G. Wilson v_

%E a(16)-a(18) from _Robert G. Wilson v_, Sep 07 2000

%E a(19)-a(23) from _Serge Batalov_, Jun 16 2020