|
%I M0545 N0195 #95 Apr 25 2023 17:30:04
%S 0,1,2,3,4,6,7,11,18,34,38,43,55,64,76,94,103,143,206,216,306,324,391,
%T 458,470,827,1274,3276,4204,5134,7559,12676,14898,18123,18819,25690,
%U 26459,41628,51387,71783,80330,85687,88171,97063,123630,155930,164987,234760
%N Numbers m such that 3*2^m - 1 is prime.
%D H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhauser, 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).
%H Jeppe Stig Nielsen, <a href="/A002235/b002235.txt">Table of n, a(n) for n = 1..64</a>
%H C. K. Caldwell, <a href="https://t5k.org/primes/search.php?Description=%5E3*2%5E%-1&Style=HTML">The Prime Pages: Database Search Output</a>
%H Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k.2^n - 1 for k < 300</a>
%H Mersenne Forum, <a href="http://www.mersenneforum.org/321search/How%20many%20digits%20these%20primes%20have.html">321 Search</a>
%H H. Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-1969-0262163-1">Lucasian criteria for the primality of N=h.2^n-1</a>, Math. Comp., 23 (1969), 869-875.
%H H. Riesel, <a href="/A002235/a002235.pdf">Lucasian criteria for the primality of N=h.2^n-1</a>, Math. Comp., 23 (1969), 869-875. [Annotated scanned copy]
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ThabitibnKurrahPrime.html">Thabit ibn Kurrah Prime</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ThabitibnKurrahRule.html">Thabit ibn Kurrah Rule</a>
%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>
%t lst={};Do[If[PrimeQ[3*2^n-1], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)
%o (PARI) is(n)=ispseudoprime(3<<n - 1) \\ _Charles R Greathouse IV_, Aug 27 2014
%Y Cf. A000043, A007505, A003307, A046865, A079906, A046866, A001771, A005541, A056725, A046867, A079907.
%K nonn,nice
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Eric W. Weisstein_, Sep 29 2007
%E a(60) = 11484018 from The Prime Pages, from _Pierre CAMI_, Nov 25 2014
%E a(61)-a(62) from The Prime Pages, from _Eric W. Weisstein_, Nov 03 2015
%E Terms moved from Data to b-file, and more terms added to b-file, by _Jeppe Stig Nielsen_, Sep 07 2021
|
