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A165779 Numbers k such that |2^k-993| is prime.

%I A165779 #32 Sep 25 2024 15:10:48
%S A165779 1,4,6,10,14,17,26,29,54,62,77,121,344,476,1012,1717,1954,2929,2993,
%T A165779 3014,3304,4704,8882,24042,43572,45722,54913,57893,72566,74473,82092,
%U A165779 117302
%N A165779 Numbers k such that |2^k-993| is prime.
%C A165779 If p = 2^k-993 is prime, then 2^(k-1)*p is a solution to sigma(x)-2x = 992 = 2^5*(2^5-1) = 2*A000396(3).
%e A165779 a(4) = 10 since 2^10-993 = 31 is prime.
%e A165779 For exponents a(1) = 1, a(2) = 4 and a(3) = 6, we get 2^a(n)-993 = -991, -977 and -929 which are negative, but which are prime in absolute value.
%t A165779 Select[Table[{n, Abs[2^n - 993]}, {n,0,100}], PrimeQ[#[[2]]] &][[All, 1]] (* _G. C. Greubel_, Apr 08 2016 *)
%o A165779 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(abs(2^n-993)), print1(n, ", "))); \\ _Altug Alkan_, Apr 08 2016
%o A165779 (Magma) [n: n in [1..1100] |IsPrime(2^n-993)]; // _Vincenzo Librandi_, Apr 09 2016
%o A165779 (Python)
%o A165779 from sympy import isprime, nextprime
%o A165779 def afind(limit):
%o A165779     k, pow2 = 1, 2
%o A165779     for k in range(1, limit+1):
%o A165779         if isprime(abs(pow2-993)):
%o A165779             print(k, end=", ")
%o A165779         k += 1
%o A165779         pow2 *= 2
%o A165779 afind(2000) # _Michael S. Branicky_, Dec 26 2021
%Y A165779 Cf. A000396, A096818, A165778, A165780.
%K A165779 nonn,more
%O A165779 1,2
%A A165779 _M. F. Hasler_, Oct 11 2009
%E A165779 a(23) from _Altug Alkan_, Apr 08 2016
%E A165779 a(24) from _Michael S. Branicky_, Dec 26 2021
%E A165779 a(25)-a(26) from _Michael S. Branicky_, Apr 06 2023
%E A165779 a(27)-a(32) from _Michael S. Branicky_, Sep 25 2024