|
%I #61 Nov 28 2023 12:52:45
%S 39,715,1983,2319,2499,3775,12819,63583,121555,121839,468523,908739
%N Numbers k such that 2^k - 7 is prime.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 39, p. 15, Ellipses, Paris 2008.
%D J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 395 pp. 55; 218, Ellipses Paris 2004.
%D Wacław Sierpiński, Co wiemy, a czego nie wiemy o liczbach pierwszych. Warsaw: PZWS, 1961, pp. 46-47.
%D Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, pp. 31, 75.
%H Keith Conrad, <a href="https://kconrad.math.uconn.edu/blurbs/ugradnumthy/squaresandinfmanyprimes.pdf">Square patterns and infinitude of primes</a>, University of Connecticut, 2019.
%H Jon Grantham and Andrew Granville, <a href="https://arxiv.org/abs/2307.07894">Fibonacci primes, primes of the form 2^n-k and beyond</a>, arXiv:2307.07894 [math.NT], 2023.
%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En-7">Search for 2^n-7</a>, PRP Top Records.
%e k = 39, 2^39 - 7 = 549755813881 is prime.
%t Select[Range[3, 20000], PrimeQ[2^# - 7] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2011 *)
%o (PARI) is(n)=isprime(2^n-7) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A096502.
%Y Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), this sequence (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).
%K nonn,more
%O 1,1
%A _Andrey V. Kulsha_, Feb 02 2001
%E a(8) from _Henri Lifchitz_, a(9)-a(10) from _Gary Barnes_, added by _Max Alekseyev_, Feb 09 2012
%E a(11) from Lelio R Paula, added by _Max Alekseyev_, Oct 25 2015
%E a(12) from _Jon Grantham_, Aug 09 2023
|
