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%I #28 Apr 07 2023 02:13:35
%S 1,4,6,10,14,17,26,29,54,62,77,121,344,476,1012,1717,1954,2929,2993,
%T 3014,3304,4704,8882,24042,43572,45722
%N Numbers k such that |2^k-993| is prime.
%C 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 a(4) = 10 since 2^10-993 = 31 is prime.
%e 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 Select[Table[{n, Abs[2^n - 993]}, {n,0,100}], PrimeQ[#[[2]]] &][[All, 1]] (* _G. C. Greubel_, Apr 08 2016 *)
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(abs(2^n-993)), print1(n, ", "))); \\ _Altug Alkan_, Apr 08 2016
%o (Magma) [n: n in [1..1100] |IsPrime(2^n-993)]; // _Vincenzo Librandi_, Apr 09 2016
%o (Python)
%o from sympy import isprime, nextprime
%o def afind(limit):
%o k, pow2 = 1, 2
%o for k in range(1, limit+1):
%o if isprime(abs(pow2-993)):
%o print(k, end=", ")
%o k += 1
%o pow2 *= 2
%o afind(2000) # _Michael S. Branicky_, Dec 26 2021
%Y Cf. A000396, A096818, A165778, A165780.
%K nonn,more
%O 1,2
%A _M. F. Hasler_, Oct 11 2009
%E a(23) from _Altug Alkan_, Apr 08 2016
%E a(24) from _Michael S. Branicky_, Dec 26 2021
%E a(25)-a(26) from _Michael S. Branicky_, Apr 06 2023
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