

A321671


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


1



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.


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(xy==p, print1(p, ", "); k=p); k++; y=3*y))


CROSSREFS

Cf. A000040, A007643, A192110.
Cf. A004051 (primes of the form 2^a + 3^b).
Sequence in context: A060274 A005235 A107664 * A085013 A164939 A125272
Adjacent sequences: A321668 A321669 A321670 * A321672 A321673 A321674


KEYWORD

nonn


AUTHOR

Jinyuan Wang, Nov 16 2018


EXTENSIONS

More terms from Alois P. Heinz, Nov 16 2018


STATUS

approved



