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Numbers k such that 19*2^k - 1 is prime.
(Formerly M2506 N0991)
5

%I M2506 N0991 #38 Nov 06 2023 14:54:35

%S 1,3,5,21,41,49,89,133,141,165,189,293,305,395,651,665,771,801,923,

%T 953,3689,5315,6989,15641,48819,78389,134053,167843,181395,311091,

%U 353661,645555,916763

%N Numbers k such that 19*2^k - 1 is prime.

%D H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%D H. C. Williams and C. R. Zarnke, Math. Comp., 22 (1968), 420-422.

%H Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k.2^n - 1 for k < 300</a>

%H Kosmaj, <a href="http://www.15k.org/riesellist.html">Riesel list k<300</a>.

%H H. C. Williams and C. R. Zarnke, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227095-2">A report on prime numbers of the forms M = (6a+1)*2^(2m-1)-1 and (6a-1)*2^(2m)-1</a>, Math. Comp., 22 (1968), 420-422.

%H <a href="/index/Pri#riesel">Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime</a>

%o (PARI) is(n)=ispseudoprime(19*2^n-1) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A032359 (19*2^k+1 is prime).

%K nonn,hard,more

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Hugo Pfoertner_, Jun 22 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E Minor corrections by _Charles R Greathouse IV_, Aug 29 2010