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Numbers n such that 137 * 2^n + 1 is a prime.
2

%I #37 Apr 06 2020 02:58:24

%S 3,27,39,83,203,395,467,875,1979,6939,13623,22835,56307,81839,197783,

%T 224879,261147,523283,533043,2457639

%N Numbers n such that 137 * 2^n + 1 is a prime.

%H Ray Ballinger, <a href="http://www.prothsearch.com/index.html">Proth Search Page</a>

%H Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/riesel1.html">List of primes k.2^n + 1 for k < 300</a>

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

%e 137 * 2^3 + 1 = 1097 is a prime so 3 is in the sequence.

%e 137 * 2^5 + 1 = 4385 = 5 * 877, so 5 is not in the sequence.

%t Select[Range[1000], PrimeQ[137 2^# + 1] &] (* _Alonso del Arte_, Apr 06 2020 *)

%K nonn,hard

%O 1,1

%A _James R. Buddenhagen_

%E 3 more terms sent by _Jud McCranie_, Jan 15 2000 and May 03 2000

%E One more term from _Jud McCranie_, Jun 12 2004

%E 533043 from _Jud McCranie_, Oct 06 2004

%E a(20) = 2457639 from _Jeppe Stig Nielsen_, Apr 04 2020