A321671 Primes of the form 2^j - 3^k, for j >= 0, k >= 0.

3, 5, 7, 13, 23, 29, 31, 37, 47, 61, 101, 127, 229, 269, 431, 503, 509, 997, 1021, 1319, 2039, 3853, 4093, 7949, 8111, 8191, 14197, 16141, 16381, 32687, 45853, 65293, 130343, 130829, 131063, 131071, 347141, 502829, 524261, 524287, 1028893, 1046389, 1048549

Offset: 1

Author

Jinyuan Wang, Nov 16 2018

Keywords

• nonn

Comments

The numbers in A007643 are not in this sequence.

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

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

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.

Examples

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

Links

• H. Gauchman and I. Rosenholtz (Proposers), R. Martin (Solver), Difference of prime powers, Problem 1404, Math. Mag., 65 (No. 4, 1992), 265; Solution, Math. Mag., 66 (No. 4, 1993), 269.

Crossrefs

Cf. A000040, A007643, A192110.

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

Cf. A063005.

Programs

PARI

forprime(p=1,1000,k=0;x=2;y=1;while(k
				

Formula

Intersection of A000040 and A192110.

Extensions

More terms from Alois P. Heinz, Nov 16 2018