login
A321671
Primes of the form 2^j - 3^k, for j >= 0, k >= 0.
4
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
1,1
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.
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.
FORMULA
Intersection of A000040 and A192110.
EXAMPLE
7 = 2^3 - 3^0, so 7 is a term.
PROG
(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))
CROSSREFS
Cf. A004051 (primes of the form 2^a + 3^b).
Cf. A063005.
Sequence in context: A005235 A353284 A107664 * A085013 A164939 A125272
KEYWORD
nonn
AUTHOR
Jinyuan Wang, Nov 16 2018
EXTENSIONS
More terms from Alois P. Heinz, Nov 16 2018
STATUS
approved