A321671 - OEIS

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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

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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

Table of n, a(n) for n=1..43.

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. A000040, A007643, A192110.

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

Cf. A063005.

Sequence in context: A005235 A353284 A107664 * A085013 A164939 A125272

Adjacent sequences: A321668 A321669 A321670 * A321672 A321673 A321674