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Wagstaff numbers that are of the form 4*k + 3.
1

%I #44 Apr 16 2023 10:39:08

%S 3,7,11,19,23,31,43,79,127,167,191,199,347,3539,5807,10691,11279,

%T 12391,14479,83339,117239,127031,141079,269987,986191,4031399

%N Wagstaff numbers that are of the form 4*k + 3.

%C 13347311 and 13372531 are also in the sequence, but may not be the next terms.

%H Jorge Coveiro, <a href="https://www.mersenneforum.org/showthread.php?t=28546">Possible 'Formula' for Wagstaff numbers</a>, mersenneforum.org.

%F Intersection of A000978 and A002145.

%o (Python)

%o from itertools import count, islice

%o from sympy import prime, isprime

%o def A361562_gen(): # generator of terms

%o return filter(lambda p: p&2 and isprime(((1<<p)+1)//3), (prime(n) for n in count(2)))

%o A361562_list = list(islice(A361562_gen(),10)) # _Chai Wah Wu_, Mar 21 2023

%Y Cf. A000978 (Wagstaff numbers), A002145 (primes of form 4*k+3), A112633, A361563.

%K nonn,more

%O 1,1

%A _Jorge Coveiro_, Mar 15 2023