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Numbers k such that (2^(2k+1) - 2^(k+1) + 1)/5 is prime.
(Formerly M1325)
0

%I M1325 #24 Jun 28 2023 14:36:51

%S 2,5,6,14,21,26,141,278,281,306,345,1365,2573,2661,4766,5385

%N Numbers k such that (2^(2k+1) - 2^(k+1) + 1)/5 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 Victor Meally, <a href="/A006556/a006556.pdf">Letter to N. J. A. Sloane</a>, no date.

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

%t For[ i=1, i<=10000, i++, If[ PrimeQ[ ( 2^(2n+1) - 2^(n+1) + 1)/5 ], Print[ n ] ] ]

%t Select[Range[5400],PrimeQ[(2^(2#+1)-2^(#+1)+1)/5]&] (* _Harvey P. Dale_, Jun 28 2023 *)

%o (PARI) is(n)=ispseudoprime((2^(2*n+1) - 2^(n+1) + 1)/5) \\ _Charles R Greathouse IV_, Jun 13 2017

%K nonn,hard,more

%O 1,1

%A _N. J. A. Sloane_

%E More terms from Douglas R. Burke (dburke(AT)nevada.edu)