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A323698 Primes of the form 3^j - 2^k, for j>=0, k>=0.

%I A323698 #30 Feb 07 2019 04:24:05
%S A323698 2,5,7,11,17,19,23,73,79,139,179,211,227,239,241,601,727,1163,1931,
%T A323698 2179,3299,4513,6529,6553,11491,19427,19681,50857,58537,58921,111611,
%U A323698 144379,176123,177019,177131,529393,545747,1593299,1594259,2685817,4782961,9492289,14346859
%N A323698 Primes of the form 3^j - 2^k, for j>=0, k>=0.
%C A323698 In this sequence, only 5 and 17 make both j and k even numbers.
%C A323698 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 3^j - 2^k = x.
%F A323698 Intersection of A000040 and A192111.
%e A323698 11 = 3^3 - 2^4, so 11 is a term.
%e A323698 41 == 1 (mod 8), 41 == 2 (mod 3), so j = 2*l, k = 2*m. 41 == 1 (mod 5), but 3^(2*l) - 2^(2*m) mod 5 is 0, 2 or 3. So 41 is not in this sequence.
%t A323698 c = 3; d = 2; t[i_, j_] := c^i - d^j;
%t A323698 u = Table[If[PrimeQ[t[i, j]] == True, u = t[i, j]], {i, 0, 20}, {j, 0, i*Log[d, c]}];
%t A323698 v = Union[Flatten[u]]
%o A323698 (PARI) forprime(p=1, 1000, k=0; x=3; y=1; while(k<p+1, while(x<y+p, x=3*x); if(x-y==p, print1(p, ", "); k=p); k++; y=2*y))
%Y A323698 Cf. A000040, A192111.
%Y A323698 Cf. A007643 (Primes not of form |3^x - 2^y|).
%Y A323698 Cf. A321671 (Primes of the form 2^j - 3^k).
%K A323698 nonn
%O A323698 1,1
%A A323698 _Jinyuan Wang_, Jan 24 2019