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Integers k such that (2^(k+3)-2^k-1)/5 is prime.
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%I #18 Jan 07 2024 23:14:57

%S 3,7,19,27,31,39,151,199,451,2371,2511,7859,103819

%N Integers k such that (2^(k+3)-2^k-1)/5 is prime.

%C If p=(2^(k+3)-2^k-1)/5 is prime, then 2^(k+2)*p is a strongly 2-near perfect number.

%H Vedant Aryan, Dev Madhavani, Savan Parikh, Ingrid Slattery, and Joshua Zelinsky, <a href="https://arxiv.org/abs/2310.01305">On 2-Near Perfect Numbers</a>, arXiv:2310.01305 [math.NT], 2023. See p. 15.

%o (PARI) isok(k) = my(x=(2^(k+3)-2^k-1)/5); (denominator(x)==1) && ispseudoprime(x);

%Y Cf. A366172 (strongly 2-near perfect numbers).

%K nonn,more

%O 1,1

%A _Michel Marcus_, Oct 03 2023

%E a(13) from _Michael S. Branicky_, Oct 05 2023