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Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.
(Formerly M2481)
5

%I M2481 #28 Jul 21 2024 21:50:29

%S 1,3,5,11,19,29,157,163,283,379,997,10141,14699,77291,85237,106693,

%T 203789,3704053

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

%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 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) for(n=1, 2000, if(n%2==1&&ispseudoprime(2^n+2^((n+1)/2)+1), print1(n,","))) \\ _Charles R Greathouse IV_, Feb 17 2017 edited by _Aurelien Gibier_ Jun 29 2024.

%Y Cf. A057429.

%K nonn,hard,more

%O 1,2

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

%E More terms from _Robert G. Wilson v_, Sep 07 2000

%E 203789 found and proved prime by _Mike Oakes_, on Sep 28 2000.

%E a(18) from _Serge Batalov_, Jun 16 2020