%I #43 Oct 13 2019 11:21:47

%S 3,5,7,13,23,29,31,37,47,61,101,127,229,269,431,503,509,997,1021,1319,

%T 2039,3853,4093,7949,8111,8191,14197,16141,16381,32687,45853,65293,

%U 130343,130829,131063,131071,347141,502829,524261,524287,1028893,1046389,1048549

%N Primes of the form 2^j - 3^k, for j >= 0, k >= 0.

%C The numbers in A007643 are not in this sequence.

%C For n > 1, a(n) is of the form 8k - 1 or 8k - 3.

%C In this sequence, only 3 and 7 make both j and k even numbers.

%C Generally, the way to prove that a number is not in this sequence is to successively take residues modulo 3, 8, 5, and 16 on both sides of the equation 2^j - 3^k = x.

%H H. Gauchman and I. Rosenholtz (Proposers), R. Martin (Solver), <a href="https://www.jstor.org/stable/2691457">Difference of prime powers, Problem 1404</a>, Math. Mag., 65 (No. 4, 1992), 265; <a href="https://www.jstor.org/stable/2690747">Solution</a>, Math. Mag., 66 (No. 4, 1993), 269.

%F Intersection of A000040 and A192110.

%e 7 = 2^3 - 3^0, so 7 is a term.

%o (PARI) forprime(p=1,1000,k=0;x=2;y=1;while(k<p+1,while(x<y+p,x=2*x);if(x-y==p,print1(p,", ");k=p);k++;y=3*y))

%Y Cf. A000040, A007643, A192110.

%Y Cf. A004051 (primes of the form 2^a + 3^b).

%Y Cf. A063005.

%K nonn

%O 1,1

%A _Jinyuan Wang_, Nov 16 2018

%E More terms from _Alois P. Heinz_, Nov 16 2018